Buddy the Elf vs Howard Langston/Rap Meanings

===Buddy the Elf===
'Twas the night before Christmas, and all through the town,
(Buddy starts his verse by parodying the classic story A Visit from St. Nicholas by Cement Clarke Moore.)
Parents fought hard so that their children wouldn't frown,
(Although in Buddy's world the toys are all made and provided by Santa and his elves, he references the classic holiday rush that is ever present throughout Howard's story.)
When they found a Turbo Man doll beneath the tree come morning,
(Following up the previous line, Buddy elaborates that many parents were out trying to find last minute merchandise related to the Turbo Man franchise, though most if not all attempts were in vain due to the popularity, with most parents having bought the gift months in advance.) 
All except for Howard Langston, who always left his family scorning!
(With the exception of Howard, of course. Howard had forgotten to buy the Turbo Man doll for his son, Jamie, when his wife Liz had initially told him to, and as such was among the crowd looking for the doll, the main plot of Jingle All the Way. Throughout the story progression, Howard is constantly letting his wife and son down.)
Looking at the run down, you're an even more rotten father than mine is,
(Walter Hobbs, Buddy's father, was a rather cynical and sour man, neglecting to spend time with his younger son, Michael, and not even being aware of Buddy's existence until the movie's present day, when Buddy was 30.)
Breaking and entering, assault, bomb accessory, now that's a naughty list!
(Howard's attempts at finding a Turbo Man doll resulted in him partaking in several illegal activities. Upon recalling that his neighbor, Ted Maltin, had mentioned the doll for his own son was nestled safely under his tree, Howard broke in to try to steal it in a last ditch effort, as well as to spite Ted. Howard also threatened two toy store employees, engaged in fisticuffs against various mall Santa's, and came close to punching a radio host. Myron Larabee, Howard's rival in the film, had threatened to utilize a bomb in the radio studio, which Howard knowingly did not stop, and as such could be considered an accessory to the domestic terrorism. Buddy refers to this list of crimes as a "naughty list," in comparison to that of Santa's. It may also hearken to the previous line, as Walter was on the naughty list.)
Raiding the kid's ball pit, impersonation, hit and run, geez! That's a lot!
(When trying to get the lottery ball to win a Turbo Man doll, Howard ended up chasing a young girl into the ball pit, causing the moms of the mall to start beating him, believing that he was a predator. After the warehouse of fake Santa's was raided by police, Howard used a toy police badge to pretend to be a private detective attempting to bust the crime ring, and later unintentionally impersonated the replacement for Turbo Man's actor in the Christmas parade. Although Howard didn't specifically cause a hit and run, he did accidentally back up into a police officer's bike.)
But your worst offense is making Jamie be the boy that daddy Claus forgot!
(The mall Santa's sang Howard a carol about a poor boy who did not obtain the gift he wanted for Christmas, titled The Little Boy That Santa Claus Forgot. Buddy twists it to say that Howard, in the role of Santa, forgot about making his son happy.)
===Howard Langston===
Oh, come on, now. You want to start by listing off my transgressions,
(Howard challenges Buddy's decision to start by listing his crimes.)
When you pave wrongdoings with your well-meaning festive intentions?
(Howard plays on the phrase regarding the path to hell being paved by good intentions. Although not explicitly mentioned, Howard is vaguely remarking on Buddy's fraudulent job at Gimbels, only caused by Wanda mistaking him for one of their employees, as well as having cut down a tree in Central Park to use as a Christmas tree.)
Your mind's like your father's failed book, it's missing a few pages,
(One of Walter's children novels was scrutinized for being published with two missing pages, resulting in children reading the novel becoming confused at how the main characters, a puppy and a pigeon, escaped an evil witch, despite Walter having believed no child would take issue with the missing context. Howard compares this to Buddy's brain, insulting his intelligence.)
You should've figured you weren't an elf with the stark difference in ages!
(The exposition of Elf discusses how humans age faster than elves, and how Buddy should have been able to figure out for himself that he was not an elf simply due to this alone.)
I'll leave you Terminated when my Turbo Time engages,
(Howard references the Terminator, another Arnold Schwarzaneggar role. He also references the Turbo Time catchphrase of Turbo Man.)
And put a restraining order out to ban you from most public spaces!
(After Buddy's brawl with a mall Santa, and subsequent firing from Gimbels, Buddy had to sign a restraining order. Howard expresses interest in having more restraining orders against Buddy be put out to ban him from public spaces. The wording also references an internet meme in which a character (although typically a real world animal) is shown with the caption "He has 97 mental illnesses and is banned from most public spaces.")
Cause you're an incelf! Buddy, just go outside and touch some grass!
(Howard combines the term "incel", an involuntary celibate, with "elf," followed up by the common internet phrase of needing to go touch grass to experience life, referencing Buddy's lack of social understanding. The line is meant to parody the song Baby, It's Cold Outside originally written by Frank Leossner. The song's woman lyrics are sung by Jovie in the shower while Buddy mumble sings the man lyrics just outside, until the end of the chorus, in which Jovie yells at him to leave upon realizing he was there. While Buddy's intentions were innocent, even claiming to not have known Jovie was nude, Howard claims that entering the women's shower while someone is showering is incel behavior.)
It took this goofy dude thirty years to get a piece of ass!
(Continuing from remarking on Buddy as an incel, Howard references that Buddy's first romantic interactions, with Jovie herself, weren't until he was 30.)
===Buddy the Elf===
Mister Freeze, where is your wife? Cause I think I last saw her with Ted,
(Once again, another nod to one of Schwarzaneggar's roles, having played Victor Fries/Mister Freeze in 1997's Batman & Robin, which actually also had its own Christmas element as well, with Freeze attempting to teach his minions Snow Miser's song from The Year Without a Santa Claus. Freeze's story is often remarked as one of the most iconic sympathetic villains due to his end goal being to save his wife, Nora. Buddy twists this to be talking about Howard's wife, Liz, and her growing closeness with Ted throughout the movie.)
He'll be your number one customer when he tucks her into bed!
(Howard is a mattress salesman, who would end calls with the line "You're my number one customer," getting so accustomed to it he accidentally said it to his wife over the phone. Buddy's line implies that Ted would be buying a mattress from Howard's own company to make love to Liz in. Tucking into bed also refers to the scene in Elf in which Buddy asks for Walter to tuck him into bed.)
===Howard Langston===
I won't stand here and take this from the worse Will Ferrell Step Brother,
(Buddy is the half-brother to Michael, though Howard twists that into being a reference to Step Brothers, a film featuring Buddy's actor, Will Ferrell, becoming step brothers with a character played by John C. Riley.)
Who let his bells Jingle All the Way when he showed them to his step mother!
(When Walter relents to allow Buddy to stay, he insists on Buddy needing to lose his elf outfit, resulting in Buddy dropping his tights, only for his step-mother, Emily, to walk into the room and accidentally see his genitals. Howard puts it in a more family friendly and thematically festive way by referring to them as "bells" and referencing his own movie's title.)
===Buddy the Elf===
Where's your Christmas spirit? Try cheering up with some carol singing!
(Buddy plays off the line Howard says to the toy store workers he threatened. In Buddy's own movie, he lives by the idea that the best way to spread Christmas cheer is singing loud for all to hear, and suggests that Howard would become happier if he did this, too.)
You must think this battle's your son's karate classes, the way you keep missing!
(Buddy deflects feeling hurt by Howard's bars by saying they miss, just like how Howard notoriously missed all of Jamie's karate classes, including his graduation to a purple belt.)
My bars are rapid fire like they're snowballs! You're a slow procrastinator!
(In his movie, Buddy and Michael partook in a snowball fight against some of the neighborhood kids, in which Buddy created and fired his snowballs rapidly. Here, he states he is doing the same with his raps. This is in contrast to Howard, who constantly put off spending time with his family.)
And your insults are a stretch, like my legs on an escalator!
(Buddy claims that Howard's insults aren't exactly true, stretching to find meaning in a way comparative to the way Buddy's legs stretched upon using an escalator for the first time, not realizing the proper way to use them.)
Smiling's my favorite, you should help your son try it sometime,
(Buddy constantly remarks on smiling being his favorite, and suggests that Howard help Jamie smile.)
Cause he can't remember the last time Christmas with you felt sublime!
(Jamie remarks that multiple Christmas parades were spent without Howard, not to mention the several times Howard was incapable of keeping his promises to him.)
I can't tell what you wreck worse: homes, cars, or your family tree!
(Buddy once again refers to Howard crashing into the police bike, but also his car being vandalized later on and needing to be towed. Homes and family tree both tie into the same double meaning. Howard's attempts to steal Ted's Turbo Man resulted in damage to the house and tree. His own inability to make his family happy almost resulted in being separated from them, meaning both his home and family would be wrecked, as well.)
While I sweetened my soured father, call me syrup on spaghetti!
(Contrast to Howard's shortcomings, Buddy was able to make his father act a better person. Buddy likens his ability to sweeten others to the sweetness of syrup, which he eats on spaghetti.)
===Howard Langston===
PUT THAT SPAGHETTI DOWN! NOW!
(In the battle, Buddy began eating his syrupy spaghetti, letting out obnoxious moans that interrupted Howard's ability to start rapping again, and angering him to the point of trashing Buddy's plate of pasta. This references the iconic scene in which Howard is on the phone with Ted, who kept interrupting Howard in a similar manner while eating cookies made by Liz, prompting Howard to demand he put the cookie down.)
Your taste in rap lyrics is as Sin-bad as your taste in cups of coffee,
(Buddy became infatuated with a coffee shop that claimed to house the world's best cup of coffee, despite Jovie's eventual disagreement that it was, in fact, a crappy cup of coffee. Howard likens this to Buddy's rap abilities, and plays off of Sinbad's name, who was Myron's actor.)
You're sitting on a throne of lies if you think you can stop me!
(A scene from Elf that became a notable meme for some time was Buddy's disgust at a fake mall Santa, and accusing him of sitting on a throne of lies. Howard flips this around to say Buddy is lying to himself about being able to stop Howard.)
I've Twinned with Danny DeVito, you discriminate against Peter Dinklage, 
(A third reference to another Schwarzanegger film, Twins, in which he and Danny DeVito played estranged brothers, with Arnold's character being one that was designed as the pinnacle of what a human could be, while Danny was the leftovers. Despite the initial differences and misunderstandings, the two characters eventually got along well and have a happy ending. Conversely, Buddy confuses Miles Finch (played by Peter Dinklage) to be an elf due to his short stature, which results in Miles beating up Buddy violently, a scene in which Dinklage utilized actual and personal anger built up from constant mockery over his size, and being cast in roles such as elves and dwarves.)
North Pole raised, yet you didn't learn to not mock people's shrinkage!
(Howard critiques Buddy's unintentional discrimination, as living in such a welcoming environment as the North Pole should have given him the morals to not make fun of people in that way, especially given the presence of shorter individuals there in way of actual elves.)
I've got Lincoln Tunnel vision on my task, you get distracted by street gum!
(When recounting his story of travelling to New York City, Buddy would interject a comedic juxtaposition of trekking through the Candy Cane Forest, and then walking through the Lincoln Tunnel. Howard plays on this with the concept of tunnel vision, one's ability to focus on the task at hand, and contrasts it with Buddy's constant state of being distracted, especially when on his way to the Empire State Building, in which the big city life constantly drew his attention, such as the aforementioned coffee shop, or gum along the street that Buddy ate despite Santa's warnings to not do so.)
How'd you manage to smash when you don't even know where babies come from?
(Howard once again insults Buddy's intelligence, claiming he likely would not know where babies came from, despite eventually bearing a child with Jovie.)
You're no real elf, and there's also no real Santa Claus,
(Howard remarks on Buddy's human nature of not being an elf, and mocks the idea of there being a Santa. This not only is meant to hurt Buddy, but also references Howard remarking on the mall Santa not being the real Santa Claus.)
That truth'll pierce your heart like your face was by raccoon claws!
(Howard explains that the harsh truth of Buddy's yuletide origins being fake will hurt his heart in a similar manner to the raccoon that attacked Buddy on his journey to New York City after Buddy tried to hug it.)