Broken Base: The Special Edition, specifically its art style. Many fans found the cartoony character designs too much of a departure from the realistic graphics employed in the original.
Additionally, of the original releases, which one is the best? Is it the more cartoony pushed-to-its-limits 16-color EGA version? Is it the later 256-color VGA version? Is it the CD version that leaves behind the old MIDI music and simplifies the UI? Is it the Amiga version that makes use of its sound capabilities and looks similar to the VGA version? Nobody really seems to agree which one is the best, and even more debates stem out of which sound card the game is best played with, some even arguing for something as minimalist as the PC speaker!
Hilarious in Hindsight: During the production of the special edition, the team planned to alter the "Buy Loom" joke due it being dated by a good decade or so at the time of release and Loom having since gone out of print. They ultimately chose to keep it out of nostalgia...only for the joke to become current again as the special edition ended up being released at the same time Loom made its debut as a digital release on Steam.
Porting Disaster: The Sega CD port of the game not only has the issue of requiring the player to navigate a PC-optimized point and click interface with a controller (which goes every bit as well as you might think), it suffers from annoying amounts of Loads and Loads of Loading as it constantly stops to get conversation and sound data in the middle of the game. The graphics are also watered down and the game runs annoyingly slow in many places (the SCUMM Bar being a particularly bad offender). They also completely left out the Visible Invisibility on LeChuck's ship for whatever reason.
Strangled by the Red String: Guybrush and Elaine. They meet once, (after he's just broken into and trashed her mansion no less) have a brief conversation, then suddenly the next time they run into each other they're acting like Sickening Sweethearts and declaring undying love! Like the rest of the game the whole thing is played very tongue-in-cheek so most players don't mind.