Broken Base: Over whether this or the second game is superior. Fans of the second tend to defend it for its lack of out-of-place time trials and having fewer vehicle levels, while fans of the third are more fond of the time travel aspect and more interesting level designs, as well as Crash's expandable move set.
Ensemble Darkhorse: Dingodile and N. Tropy, both because of their designs, the roughness of their Boss Battles and their quirky accents. Dingodile started showing up quite a bit, and Tropy actually took Cortex's place for one game. Sadly, with the Radical Entertainment games, both have developed a case of Chuck Cunningham Syndrome (while Dingodile appeared as a boss in the portable versions of Crash Of The Titans, while N. Tropy's final appearance was as a minor antagonist in Twinsanity).
Franchise Original Sin: One of the major complaints about The Wrath of Cortex (aside from It's the Same, Now It Sucks) was its heavy reliance on vehicle segments. This issue can actually be traced as far back as this game, as a lot of the levels here were done on vehicles (especially the motorcycle which had four levels dedicated to it), more so than the previous two games. However, it was still nowhere near to the extent that Wrath of Cortex would end up doing.
Game-Breaker: The Fruit Bazooka is this, since now you can aim away at the crates without personally going there, as well as hitting enemies from far away. Not so much for Time Trials, though.
Crash's death animations are usually Played for Laughs, but when he gets hit by one of N. Tropy's energy balls (or by colliding into the flying saucers of the future levels), he explodes into several particles and disintegrates out of existence. There's nothing silly about it. It's played unnervingly straight.
Scrappy Mechanic: Activating the Nitro Detonator crate in a level - just like in the previous game, any offscreen Nitro destroyed like this won't take out any adjacent crates if you didn't break them. And three levels, Gone Tomorrow (level 21), Flaming Passion (level 23) and Rings Of Power (level 28) don't even have Detonators while having Nitro crates, as the game expects you to destroy them by fruit bazooka (first two examples) or plane (last one). Have fun replaying the level if you're going for the gem for destroying all crates and didn't know this.
N. Gin can be this to some players. For one thing, it's an Unexpected Shmup Level, and the control is actually reversed from the regular shmup levels (i.e tilting your joystick right will make Coco fire to the left). In the second phase it gets worse because after getting used to the destructible missiles, he adds in projectiles that can't be destroyed.
Cortex unlike the last game. He wouldn't be too difficult on his own, but in addition to fighting him the player also has to avoid being killed by attacks thrown by Aku Aku and Uka Ukua's fight. Also unlike the rest of the game, the player doesn't get Aku Aku for the fight so they die in one hit.
That One Level: Tomb Wader, especially on Time Trial mode. Hint: Rising water levels.
That One Sidequest: Getting all of the gold or platinum relics which gets you a hidden gem.
They Wasted a Perfectly Good Character: Coco's "playability" is completely superficial, limited to vehicle levels or four or five steps of slow walking. Those getting Warped to play a fresh new character will be sorely disappointed. This is rectified in the N. Sane Trilogy, however, where her playability has been greatly expanded to almost all levels from this game (as well as being playable the first two).
The boss fight against the new time-twisting villain N. Tropy. Does he use manipulation of time to move obstacles around in previously-unseen ways, or transfer himself and Crash through different game locales as the fight rages on? No, he just shoots beams and chucks some electrified clocks at Crash.
Compared to otherplatformers, which make unique use of altering time, Warped only implements the concept nominally to introduce historically themed levels, instead of adding gameplay elements of time-travel.