Skyrim:Scoundrel's Folly

Quick Walkthrough
#Speak to Mercer Frey.
#(Optional) Speak to Brynjolf.
#Speak to Gulum-Ei.
#Retrieve a case of Firebrand Wine from the Blue Palace.
#Return to Gulum-Ei.
#Follow him from a safe distance.
#Confront or negotiate with Gulum-Ei.
#Return to Mercer.

Detailed Walkthrough
The Plot Thickens
When you next speak to Mercer, he will remark that the symbol found on the Goldenglow Bill of Sale from Goldenglow Estate is the same as the one on the Promissory Note found at the Honningbrew Meadery, leading him to the conclusion that the Thieves Guild is not, in fact, cursed (as Delvin believes) but is in fact being deliberately acted against by an unknown competitor. Mercer will also reveal that a name mentioned on the Bill is the alias of a former contact of the Guild: an Argonian dockworker for the East Empire Company named Gulum-Ei.

Nothing Gets You Nothing
Mercer will send you to the Winking Skeever in Solitude to shake down Gulum-Ei for information regarding the sale of Goldenglow Estate: namely, its purchaser. However, Gulum-Ei is used to dealing with Thieves Guild thugs, and will not forfeit his information easily, out of fear for his own safety. To successfully persuade him, you need a Speech skill of at least 75 (or 53 with the persuasion perk). Intimidation will always fail.

If you cannot persuade him, you need to bribe him, although you won't offer him gold as is standard with the bribe option; you have to perform a small theft instead. A buyer of his is looking for Firebrand Wine, and there happens to be a case of it up at the Blue Palace; Gulum-Ei looks to you to steal it for him.

The wine itself is easy enough to retrieve. Once you've walked in through the front door of the Palace, the case of wine is sitting on an end table in a corridor to the left of the main staircase. You will know the case because of the 'Firebrand Wine' label clearly pasted on the side of the crate. Quickly and quietly pocket the wine and head back to the tavern to get your critical information.

You Didn't Hear It From Me...
When you hand over the wine or were otherwise able to convince him, Gulum-Ei sees fit to compensate you for the effort, and hands over an assortment of Soul Gems as payment. Afterwards, he explains that he was approached by a mysterious woman, who gave him a large sack of gold with which to buy Goldenglow Estate. No name was given, but Gulum-Ei mentions that she was extremely angry, and that this anger was directed at Mercer Frey in particular. With nothing else to say on the matter (despite your suspicions to the contrary) Gulum-Ei takes his leave, declaring your business done.

Tailing the Argonian
You will need to follow Gulum-Ei as he leaves the tavern, as you believe he is not wholly forthcoming about the information he has. If he spots you, he will insist that he told you all he knows, and will tell you to stop following him. Eventually he will lead you to the East Empire Company Warehouse, where he works and used to steal goods for the Thieves Guild. Here, you can use the tops of the shelves and stacks to follow him at a close distance without him detecting you, since he will keep to the ground floor. Most of the wall torches lighting the pathways can also be picked up, making it much easier to sneak. The warehouse is also patrolled by mercenaries paid for by the company, and they will attack you on sight. Proceed cautiously and at a distance, as Gulum-Ei is on edge and may occasionally pause to look over his shoulder as if expecting to be followed. Alternatively, you could wait until Gulum-Ei gets far enough ahead of you, and then just kill the wardens if they spot you. At the far end of the warehouse, Gulum-Ei will turn around and head back the way he came, so quickly duck out of sight behind a nearby shelf or keg. Gulum-Ei will then take a set of steps down into the water, and around behind a shelving unit to a hidden pathway, leading to a door into Brinewater Grotto. If you lose sight of Gulum-Ei, the entrance to Brinewater Grotto can be hard to find.  After passing the huge barrel, go down the stairs into the water and really hug the stone wall.  You will see a smooth, narrow ramp in the wall that will lead up out of the water by shelving units, then into Brinewater Grotto.  

Once you follow him into Brinewater Grotto, the quest will update, instructing you to confront Gulum-Ei; tread carefully, as the cave is littered with traps and bandits. While the Thieves Guild frowns upon killing on the job, the bandits are fair game, and you can either fight them toe-to-toe or systematically take them out with sneak attacks. There is also a chest hidden in the water past the second two guards to the left of the path with some valuable goods in it. When you reach the end of the cave, speak to Gulum-Ei and he will reveal the name of the mysterious antagonist to the Guild: Karliah, the thief who murdered the previous Guildmaster, Gallus.

If you speak to Gulum-Ei again and tell him that he owes you, he will inform you that he will now act as a fence and buy any stolen items you bring to him as his way of repaying you for sparing him.

There are three levers next to the gate. They open the two empty cages and a secret door to the rear of the cavern. Three Horkers may attack in the grotto beyond, but the path leads to the exit to the outside. Return to the Guild for your pay and to tell Mercer your findings. He is (understandably) upset, and deduces where Karliah will be next: a ruin far to the north of Riften known as Snow Veil Sanctum. And for this, Mercer insists that he comes along on your next job...

Killing Gulum-Ei
If you do not wish to go to the trouble of tailing the Argonian, you may simply kill him. It is recommended that you kill him stealthily as to avoid incurring a bounty.  If and when you kill him you will receive a new objective: "Find alternative source of information." Proceed through the quest exactly as detailed above and where you were supposed to talk to Gulum-Ei there will be a chest with a written confession instead. If you kill him after following him, the note will be on his body; you must read the note in order to advance to the next objective.  If you kill him there is no need to sneak around the guards in either the East Empire Company warehouse or Brinewater Grotto. This makes this mission significantly easier to complete for a non-stealthy character, but you will forfeit the payment and you will not have Gulum-Ei as a fence later on.

Reward
Mercer Frey will speak with Tonilia and arrange to have a piece of your Thieves Guild armor upgraded. Note you only get to pick one piece:
Thieves Guild Armor - +1 Armor, increases carrying capacity from 20 to 35.
Thieves Guild Boots - +1 Armor, increases Pickpocket from 15 to 25.
Thieves Guild Gloves - +1 Armor, increases Lockpick from 15 to 25.
Thieves Guild Hood - +2 Armor, increases Barter effect from 10% to 15%

Notes
If you are friendly with certain members of the Blue Palace, you can take the case of Firebrand Wine without it being marked as stolen.
The quest marker for the "Follow Gulum-Ei" objective will update automatically, allowing you to follow him at your leisure.
Being spotted by Gulum-Ei while tailing him will not result in failure. He will just stop until you retreat out of detection range.
In the office overlooking the warehouse is the East Empire Shipping Map, which Delvin will pay a leveled amount of gold for.
Gulum-Ei will not be available to trade with until you return to Mercer and finish the quest.

Bugs
 
 
As of patch 1.4, all pieces of Thieves Guild armor are also available in The Ragged Flagon - Cistern.  If you have also sold all of those pieces, just wait somewhere outside of the Ragged Flagon, then return and obtain a newly-spawned copy.
 
 You can either open the console just after leaving the Winking Skeever and type   followed by   to move him back inside the walls to your location, proceed to Brinewater Grotto to the room with 3 switches and use the same code (  followed by  ) or try loading a game few times again.  Do not try talking to him elsewhere before this point, as it will glitch the quest completion.
 
This is solved by waiting for the next day in another location.
 
 

Quest Stages