Awesome Art: It's widely agreed that the animation is one of the film's biggest assets. It's often been likened to "a good plate with nothing on it."
Big-Lipped Alligator Moment: The train scene in the beginning, after it, Nemo never mentions it again. Granted, it's somewhat justified being a dream. Perhaps he forgot it after waking up.
Cross-Cultural Kerfluffle: Having been produced in Japan, the filmmakers clearly were clueless that the character Flip looking just like a black-faced minstrel (even though faithful to Winsor McCay's original work) would be extremely problematic for modern international audiences. Gene Siskel and Roger Ebert even pointed this out in their review. They at least had the foresight not to include Imp, a much more blatant racial caricature from the comic, while Flip could at least be explained away as a clown.
Idiot Plot: Hoo boy. This trope being present could be excused by the story (probably) taking place in a little boy's dreams, but if Nemo had kept his darn promise not to open one particular door, then he'd have saved the kingdom a lot of grief. Going backwards a step, King Morpheus could have been the one to save the kingdom some grief by not entrusting a little kid he just met with a key to the kingdom - or at the very least telling him why he shouldn't open the door. Taking things back even further, King Morpheus could have simply chosen his own daughter as his heir, instead of recruiting some random boy from the real world, but apparently Slumberland is a fantasy dream kingdom that adheres to male-exclusive succession, completely barring the possibility of a ruling queen.
Nightmare Fuel: It would have done Tim Burton proud. It can be rather amusing in retrospect that Nightmare Land, where all nightmares come from, can be considered Nightmare Fuel. Or: A fictional world responsible for all nightmares in a fictional Earth is also responsible for nightmares in the real world.
Nemo's nightmare of the train at the beginning most definitely is this in its rawest form.
The nighmarish essence that Nemo accidentally lets loose when it kidnaps King Morpheus. It most definitely will keep your kids up at night.
Visual Effects of Awesome: For all its faults, the animation is nothing short of pure eye candy and enjoys the quality that can match that of a Studio Ghibli film. The designs of Nightmare Land and the many nightmarish visions we see are especially striking.