During the first level of the game, if Crash keeps going through a certain amount of times without getting the level's crystal, Cortex will become frustrated with him each time he comes back without it.
In the North American version of the game, Tiny Tiger is erroneously listed as Taz Tiger in the pause screen. The European version fixed this.
The original game Crash Bandicoot (1996) is considered a really difficult game. Naughty Dog realized the concerns with the series' difficulty and made this sequel, as well as all of of the games in the series, a bit easier in gameplay.
If you don't move for about 30 seconds, you can see that Crash can do his old animation from Crash Bandicoot (1996).
The first game to have crystals.