Although in my opinion this is one of the lesser musicals of stars Frank Sinatra, Gene Kelly, Kathryn Grayson and director George Sidney, a lesser musical featuring anyone from that line-up is nothing to sneeze at, and in conjunction, the line-up makes Anchors Aweigh a pretty good film despite its flaws.
Sinatra and Kelly are Clarence Doolittle and Joseph Brady, respectively, two Navy men. As the film begins, they're just pulling in to the Los Angeles area for some much needed leave. Brady plans on visiting a girlfriend named Lola. Doolittle is still a bit wet behind the ears, appropriately enough, and seeks advice on women from Brady in private (publicly, scriptwriter Isobel Lennart and Sidney have all of the Navy men comically exaggerating their finesse with women to each other). Brady promises to help get Doolittle hooked up, but primarily because Doolittle won't leave him alone otherwise. A kink is put into their plans when local police basically force them to assist with a young boy who is obsessed with the Navy. He won't give the police any information about who he is or where he lives. Brady helps and he and Doolittle end up taking the boy back home. When the boy's guardian, Susan Abbott (Grayson), finally shows up, Doolittle goes gaga for her. Brady tries to convince him to forget about her; Brady just wants to get back to Lola. But they keep getting coaxed back to Abbott's home, and eventually something of a love triangle forms. Things become more complicated when Brady lies about Doolittle knowing a famous musician, Jose Iturbi, who is in residence at a film studio, and claims that Doolittle has set up an audition for Abbott, who is a singer and actress, in front of Iturbi.
Because of the story, the music is a strange combination of militaristic music--because of the Navy premise, obviously, Broadway pop--what the stars tend to sing in more informal settings, opera--what Abbott's character excels at, Liberace-like popular classical--what Iturbi did, and Mexican music--because Abbott frequents a Mexican restaurant in a Mexican section of L.A. The combination doesn't work as well as it could. Plenty of the songs are good, and everyone involved is certainly talented as a singer or musician, but the genre hopping tends to lose coherence. Worse, there are a couple showcases for Iturbi, who was apparently a big star at the time, that effectively bring the plot to a halt and that seem more than a bit hokey at this point in time. I just watched another film that happened to have outstanding music, Robert Altman's Kansas City (1996), but that misguidedly stopped the plot to periodically turn into a concert film. Anchors Aweigh takes a similar tactic. Yes, this is a musical, but there's a difference between songs that propel and are integral to the plot and concert showcases that seem like contractual obligation material.
There are also some plot problems. It's not very well established why Brady is so against Doolittle's pursuit of Abbott. We can guess that Brady thinks Doolittle shouldn't become involved with someone who has to take care of a kid, and who seems relatively "proper" and traditional, but on the other hand, Brady can tell that Doolittle doesn't have the same womanizing disposition that Brady admits of himself. Abbott seems like a good fit for Doolittle, and furthermore, Lennart works hard to establish that Brady just wants to get Doolittle out of his hair and get on with meeting Lola--it seems that Brady's character should be quickly pawning Doolittle off on any candidate, whether she's a good fit or not. This might seem like a minor detail, but it's actually the hinge for about a third to half of the plot. The story also seems a bit drawn out. Length is a problem. Anchors Aweigh, clocking in at roughly two hours and twenty minutes, should have been cut down by at least a half-hour.
The above surely sounds like I'm complaining about the film too much to justify an 8. I just wanted to stress what I see as flaws, because the conventional wisdom on Anchors Aweigh is much closer to the idea that it has no flaws.
Sinatra, Kelly and Grayson are certainly charismatic, separately and together. They turn in good, interesting performances. Sinatra looks and acts much younger than his actual age of 29  30 while shooting. He plays an unusually naïve, virginal character--completely different than most of the roles he would take later, and different than his public image as a crooner. For Kelly, this was his breakthrough film, and rightfully so. His choreography is varied and impressive, as is his acting. Grayson is charming, her performance is sophisticatedly understated, and she's simply gorgeous. All of this helps override the flaws with the script and the drawn out pacing.
And there's even a very interesting element that probably only arises because Sidney was allowed to sprawl over a large variety of moods--the infamous Kelly dance with Jerry the Mouse (of "Tom and Jerry" fame) in an extended fantasy sequence. This is one of the earliest examples of combining live action and animation, and it is extremely well done and enjoyable as long as you're a fan of fantasy. The fantasy sequences tend to be the best of the film. Matched in excellence to the dance with Jerry the Mouse is a long song and dance number featuring Kelly and Grayson, where Brady is imagining Abbott in a scene from a period film while he woos her, having to resort to acrobatic stunts to reach her physically as she stands on a high balcony.
As uneven and flawed as the film is, it is largely successful and entertaining to watch. Fans of classic musicals certainly shouldn't miss Anchors Aweigh, and neither should Sinatra fans, who'll get quite a kick out of his character.

Even though this was a made-for-TV production, there's absolutely no excuse for the rock bottom results of the finished product. This movie DID have a budget and it had a casting department, so, if you're going to make a movie about a true life story, and actually put "the true story" in the title, shouldn't some effort be put forward to try and capture some realism ? First of all, this movie is absurdly cast. These actors belong in daytime television soaps, or in those ridiculous Lifetime channel movies, and not in a real-life gangster/criminal tale. Everything about them, from their looks to their mannerisms, just screams of the 90's-shopping-mall-alt-rock-listening generation. What about the script ? Two words describes it - stupid and insulting, and again it's way too 90ish sounding. I don't think the real Clyde Barrow ever uttered the words "I'm outta here." It's as if a bunch of "New Kids on the Block" fans got together and decided to make a really "kewl flick" about Bonnie and Clyde, you know, one that would be totally rad and rockin'. Well, this sticker doesn't even rank on the rad and rockin' scale. Everything that can be wrong with any kind of film is wrong here, from the casting and acting to the editing and music. Every single thing is grossly wrong....and it's infuriating that the parties responsible for this atrocious turkey had the nerve to put "the true story" in the title. It's certainly NOT the true story, but even worse, it's not even remotely entertaining as a mindless popcorn flick that's accepted on its own terms. Like I stated in my heading, it's simply horrible beyond words, on every level imaginable. Trust me on this, or watch at your own risk.