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, N Tropy's final appearance was as a minor antagonist in Twinsanity).
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.
Good Bad Bugs: It's possible to exploit a glitch involving the game's demo to start a new game with all upgrades without having to defeat any bosses beforehand, making the game more easier.
Hazy Feel Turn: While not a good guy specifically, Tiny seemingly worked for N Brio in the previous game and only attacked Crash to prevent him helping Cortex's plans. From this game onwards he serves Cortex, to the point of being his most loyal minion after N Gin.
However, since the main point of Cortex Strikes Back was Cortex lying to Crash about who's side he and N. Brio were on, it's entirely possible Tiny was Cortex's minion all along. Tiny's battle in CSB being fought in a specific area that looked like Cortex's spaceship could be a Red Herring or Cortex laying an early trap for Crash. It's difficult to say.
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: You have to wait nearby after activating a TNT-crate's timer, since if you just go on afterwards, only its explosion records in the level's crate count, without destroying anything next to it.
Even for a how little time you control her, it is less efficient to play as Coco than Crash in the Chinese levels since her slow walking could add on a couple seconds to Time Trial records.
Stop Helping Me!: While Crash fights Cortex, Aku Aku keeps Uka Uka busy by dueling with him. Their battle can actually kill Crash if he gets caught in the crossfire, and is in fact the main obstacle of the fight. Not only that but this means you can't get a protection from Aku Aku.
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.