The Wrath of Aku Aku (submitted by Micster): Like in the Japanese versions of the original trilogy, Aku Aku will tell you a hint when you open one of his Crates. This time around, there are much fewer hints (around 6 per Warp Room). Also, the animation is the same every time, without proper lip synching.
(Xbox Loading Screen)
Loading Screen: The loading screen varies depending on the console. In the PS2 version, it shows Crash falling in a multi-coloured warping vacuum. In the Xbox version, the same happens in a different angle, but the vacuum is green. In the GameCube version, it's just a plain black screen with the word "LOADING" flashing (essentially the same as the very first loading screen you get when you boot up the PS2 game).
Cortex Health Bar: In the final boss fight, "Crunch Time", there isn't any health bar in the PS2 version. The other versions have one for Cortex, showing his entire body rotating next to it.
Coco's Shadow in Banzai Bonsai: When you go behind the thin panels after the maze, Coco's shadow can be seen on them, as a result of lighting. This effect isn't present in the GameCube or Xbox versions.
The Main Computer: The big computer from the VR Hub System usually has a floating ring that leaves a trail of sparks on the right side. It was replaced by simple cables in the GameCube version.
Colourful Crunch Time: In the PS2 version of "Crunch Time!", the screen changes its colour according to which Elemental is being used. This effect is not present in the other versions.
Graphical Glitches: The GameCube version has a few visual glitches during the ending cutscene. Aku Aku's feather sprites and Pura's moustache sprites aren't transparent, meaning they appear as coloured rectangles. Additionally, Crunch's lighting during the second half of the ending is grossly off, making him look a lot darker than everyone else.
Music (by e122psi and Smaz): The music in the PS2 version pauses briefly before looping back to the beginning. The only level where this doesn't happen is Medieval Madness. This was fixed for the GameCube and Xbox versions, but interestingly, Medieval Madness had its music replaced by that of The Gauntlet in those. The reason for this is unknown, but there seems to be a correlation between it being the only properly looped track in the PS2 version and its posterior disappearance, somehow.
Medieval Madness (by Smaz): As mentioned, Medieval Madness had its music track replaced by the one from The Gauntlet in the GameCube and Xbox versions. Additionally, there were a couple of odd layout changes: the two big platforms just after the treacherous wooden ramps were reduced to a single one. After the wobbling platforms up ahead, you can encounter an elevator in the wall. It moves much slower in the GameCube and Xbox versions.