CTR tokens: Remember the Silver Coin Challenges in Diddy Kong Racing? Well, they're back, but this time you only need to get 3 letters in each race.
Relics: Similar to Crash 3, the courses are littered with time-stopping crates. Finish 3 laps with a good time for a sapphire or gold relic. Or platinum.
There's also bosses and multi-race cups through the adventure, and the battle arenas are converted into contests where you have to get all the crystals in the arena before running out of time (which is cut if you hit a Nitro crate).
Tropes used in this game:
100% Completion: You have to complete all the tracks, get all the CTR tokens, all of the relics (including platinum!) and defeat all of Oxide's ghosts in time trial. At least, Beating all of Oxide's ghosts unlocks the scrapbook you get shown if you complete Adventure mode in the main menu.
Ash Face: Getting burnt by any obstacles in the course only results in spinning out for a moment before shaking off the soot.
The Bad Guy Wins: Oxide states that if he wins, he will turn Earth in to a giant concrete parking lot. Obviously he doesn't, but Battle Mode provides a hypothetical "What If?" scenario by naming one of the unlockable areas Parking Lot.
Big Fancy Castle: Cortex Castle, the battle map Nitro Court, and the hub world Citadel City.
Oxide is also immune to traps and missiles, merely spinning just like when hit with the chemicals rather than tumbling like with the TNT and Nitro.
It's implied that the bosses sans Oxide are cheating bastards because Oxide is an even bigger bastard than the other four; they have to make sure that you'll be up and prepared against Oxide's dirty tricks. Evidenced in the Purple Gem Cup where they race together with you normally with the same rules as a normal enemy racer.
Crutch Character: Polar, Pura, Ripper Roo, and NSTC!Penta Penguin. They have good handling, but have inadequate top speed. As such, they are extremely slow initially, and they are not the quickest accelerators either, but they can make turns without slowing down that require faster characters to powerslide or brake, and thus are the best options to learning how to handle the more complex maps.
Double Unlock: To get to race Oxide for a second time and beat the game, all you have to do is beat the time trials on every course. Easy, right? Well, that includes a track that's only unlockable if you collect all five gems. How do you get those? Beat a cup race, four races in a row for one gem. How do you unlock those? Collect 4 tokens of the cup's respective color by beating races and collecting letters around the course.
Easy Level Trick: In the form of shortcuts. Some are intentional (e.g Crash Cove, Tiger Temple, Cortex Castle), a few others are not (e.g Hot Air Skyway, Oxide Station).
Enemy Mine: Everybody teams up against Oxide to save the world; most of the playable roster is made up of bosses from the previous games, in fact. That said, they are competing to be the one who races Oxide. Even the bosses (except for Oxide, of course) are really on your side and are essentially sparring partners. Their job is to make sure that Earth's champion is actually capable of defeating Oxide, because the entire planet loses if the champion loses.
Flawless Victory: Getting all the time-freezing crates in a time trial rewards a 10 second deduction from your final time.
Fragile Speedster: Coco, N. Gin, and Pinstripe all are high-acceleration karts. Because of this, they reach their top speeds faster and recover from hits faster as well. However, said top speed is not very high, and their carts handle worse than those of balanced characters.
Some of the tracks are based off of Mario originals as well, mostly those from Mario Kart 64. For example - Coco Park is like Luigi Raceway, while Tiny Arena is similar to Wario Stadium. A really clear one is Cortex Castle, a go-cart race through the castle of the series' (usual) Big Bad filled with right-angle turns.
The items follow the same formula for the most part. Rockets instead of red shells, clocks instead of lightning, warp orbs instead of blue shells, Bowling Bombs instead of shells, Chemical beakers and TNT instead of banana peels, etc. Differentiated in that they get boosted if you have 10 wumpa.
In the other direction, CTR brought back some Mario Kart features into 3D that only appeared in Mode-7 Mario Karts until Wii: namely, not having to wiggle the stick for drift boosting, and having speed-increasing pickups on the field. It also had a system where hopping off a jump gives a racer a boost upon landing, just like the trick system found in Mario Kart Wii and later.
Go Karting With Neo Cortex: Justified by way of Enemy Mine. There are actually more bad guys than good guys as playable characters! You start with 4 bad guys and 4 good guys, then the unlockables are mostly the bosses in the Adventure Mode. In total, there are five good guys (the four Good defaults and one unlockable) and ten bad guys (the four Bad defaults plus six unlockables).
Jack of All Stats: Crash, Cortex, Fake Crash, and Komodo Joe all have balanced stats. They can power slide adequately in straight lines, and maintain a good top speed accordingly. Their acceleration and handling are also solid, which means their maneuverability and time taken to reach top speed are what would make them stand out from karts that have really good top speed but poor acceleration and handling.
Also Penta Penguin in the PAL version of the game, having top stats all round.
Magikarp Power: Polar and Pura initially start out as this, in Adventure Mode. Their karts do not have much in the way of top speed, and power sliding in a straight line is a troublesome task for them. After Papu Papu's boss fight is when tracks turn out more favorably for the handling-centric karts and the game gives myriad opportunities for them to come out on top. Notably, tracks such as Dragon Mines and Hot Air Skyway are turning-centric. While they would normally be difficult for someone without stellar handling, Polar and Pura have karts which make those tracks a breeze for them.
Man-Eating Plant: There are these in Papu's Pyramid, although the worst you suffer from them is lots of lost time.
Master Of All: In the PAL version, the cheat-only character Penta Penguin has perfect scores in all stats. When it comes to the race itself, though, he's often tiered lower than the high-speed-low-handling characters, due to how power-sliding works.
May Inca Tec: Papu's Pyramid. Also the battle map Rampage Ruins and the hub world both tracks are placed in, The Lost Ruins. To some extent, Tiger Temple.
Mighty Glacier: Tiny, Dingodile, Papu Papu, and N. Tropy are all heavyweight karts with exceptionally good top speed. Because they're heavyweights, however, their handling suffers and they take their time to reach top speed.
Difficult but Awesome: Once power-sliding is mastered, however, those guys can remain on their top speed the whole race, trivialize turns, and even, thanks to the low handling stat, even powerslide in straight lines without losing time.
Non-Fatal Explosions: No matter how many Nitros, chemicals, TNTs, bombs, missiles, or electro-balls (that work like the Blue Koopa Shell in Mario Kart) the racers get hit with, the worst they get is a tumbling and then they always eventually land wheels-down to continue.
Nostalgia Level: Lots. A few examples: Blizzard Bluff is one to the snow cavern levels in Cortex Strikes Back, and N. Gin Labs is one to the lab levels in the very first game.
Not Just A Tournament: At the start, the cast just races for the fun of it, but then Oxide comes and threatens the whole planet to become slaves unless their racing champion can beat him at racing.
One Stat to Rule Them All: Due to how power sliding works, acceleration tends to not be much of a factor for a good player, who will remain at top speed the whole race, and having a high turning stat may prove to be hindering, preventing a character from power sliding in a straight line (sound familiar?); so characters are tiered pretty much based on their speed.
Palm Tree Panic: Crash Cove, the battle map Skull Rock and the hub world N. Sanity Beach.
Purposely Overpowered: Attempted with Penta Penguin in the PAL version. However, due to poor handling actually being an advantage, he's not actually top tiered.
Regional Bonus: Penta Penguin, the secretmost character, is a run-of-the-mill beginner character in the NTSC version, but, in the PAL version, has all stats maxed out.
Sacrificial Planet: It's revealed that Nitros Oxide is the cause of the barren wasteland on Mars: the inhabitants on the planet failed to defeat him at racing and thus get decimated. He threatens to do the same on Earth (by making the planet a parking lot and slaving all its inhabitants) if they failed to defeat him at racing, too - setting up the story.
Schizophrenic Difficulty: The tracks in Adventure Mode aren't placed in ascending difficulty. Many times, the courses are chosen because it fits into the theme of the world rather than difficulty. This is why, for example, Coco Park is in the second world when it's probably the easiest track, or why Papu's Pyramid is in the second world when it's a pretty hard track. The Arcade Mode cups fix this and the tracks are in ascending difficulty.
Secret Character: Penta Penguin is the only character who must be unlocked with a cheat code. The other hidden characters can be unlocked via cheat codes or accomplishing in-game tasks.
Shark Tunnel: Most of Roo's Tubes takes place in one of these.
Slippy-Slidey Ice World: Blizzard Bluff and Polar Pass, as well as the battle map The North Bowl and the hub world Glacier Park.
Took a Level in Badass: Every item has a "juiced-up" version if you have the maximum 10 Wumpa Fruit (which are scattered around the course and also slightly increase your speed, like coins in classic Mario Kart).
PAL!Penta has souped up stats everywhere, making him quite the speed demon.
Wake-Up Call Boss: Papu Papu, to racers who aren't Tiny or Dingodile. Top speed is his primary stat, and Papu's Pyramid does not offer much of a disadvantage for him as most of the turns needed are still wide enough for him (and Tiny/Dingodile) to make without much of an issue. The map is significantly more difficult than other levels within the same mini-hub. Papu Papu's traps are the N. Brio beakers, which provide more of a notorious hazard than any of the other bosses' traps as they are hard to dodge and cannot be shaken off once hit. After Papu Papu is defeated, the game's Adventure Mode begins to shape up.
Warm-Up Boss: Ripper Roo is a character with low top speed, a high handling that wouldn't do him any good in his challenge map, as said map (Roo's Tubes) is one of the simplest and most straightforward in the game, and his trademark TNT traps can be easily shaken off.