Annoying Video Game Helper: The Cheshire Cat. Less annoying than other examples since you actually have to summon his help but, the character's eponymous quirks being what they are, his "help" is often enigmatic to the point of uselessness.
A good majority of the soundtrack, thanks to the musical talent of Chris Vrenna (who now plays with Marilyn Manson). The best example would have to be either "Village of the Doomed" or "Flying on the Wings of Steam", the latter of which had a remix that was put on the album.
Goddamned Bats: The Snarks that jump out of lava to spit fire at you. They're very hard to kill without homing weapons like jacks or cards since lava is life-draining to the touch. The regular Snarks are pretty annoying too, frankly.
Game-Breaker: Once you get the Jacks, they'll pretty much be your most-used weapon. That is, until you get the Jabberwock's Eye Staff, which works wonders on larger groups of enemies.
The death of the Cheshire Cat is sad, but the weird squeak/meow noise he makes when it's happening is hard not to laugh at.
That One Level: Exactly which one qualifies tends to be fairly divisive, but there's a few that standout more than others:
Wholly Morel Ground, on account of being a level spent entirely underwater and requiring Alice to follow the mock turtle. While significantly less hard (and more short) than others that count, it can certainly feel tedius.
The Majestic Maze, purely because you can make the entire level unwinnable if you make the mistake of using the Watch before Alice needed to do so (forcing you to replay the entire level).
That One Boss: The Jabberwock in the second battle. He attacks from the air, directly from above you (which is nasty enough in TPP shooter) and his primary attack sets you on fire, causing Alice to flail and scream.
Rated M for Money: Apparently, Alice's insanity means violence, bloody decapitations, sorts of stuff Alice probably wouldn't have imagined by that point in her life (considering she was catatonic after all), and the ads seemed to merely show that this is not the family friendly Alice in Wonderland that Lewis Carroll gave us. Apparently, Executive Meddling is to be blamed for this, since American McGee himself has stated in an interview that the developers were pushed to make the game a lot Darker, Edgier, Bloodier and Gorier than they had originally envisioned it. But then again, this is not necessarily a bad thing.