Broken Base: The whole "two drivers at one time" mechanic. Either it's one of the most innovative features to be introduced to the entire Mario Kart franchise and needs to make a return, or it's one of the worst aspects about Double Dash and it's a good thing it has yet to be brought back. There are also those who were completely indifferent to the whole mechanic, but there have been some debates among fans of the first two camps on if the feature should or should not return in a future entry.
The lightweight characters are by far the most used due to being out-and-out Game Breakers with karts that have very high acceleration and handling, and are tough to hit with items. The crown however goes to Baby Mario and Baby Luigi, as they also have a devastating Special Item in the form of the Chain Chomp.
In particular, the Barrel Train, Diddy Kong's specialty kart, is the best kart in the game. Despite what the in-game stats might tell you, it's tied with some heavyweight kartsnote and the Bullet Blaster for the fastest kart in the game, and it loses the least amount of speed when travelling off-road. Although its acceleration is the worst of its weight class, it's still only average, and it's also the heaviest light kart in the game. Along with it's low traction (which makes it still retain a lot of speed if it slips over certain items like Banana Peels), these traits make this kart a very popular pick in Time Trials.
Koopa and Paratroopa's special items are triple red and green shells, which are normally items anyone can get, but in this game they have exclusive access to them. The Chain Chomp might be powerful, but it doesn't come close to the Boring, but Practical "more things to throw at the enemy / destroy oncoming projectiles with".
Franchise Original Sin: in Mario Kart 64 and its GBA successor, Super Circuit, the Blue Shell worked like a red shell, but it hit every driver in front of the one who threw it and finished with the one in the first place; this game, however, marks the debut of the (much more hated) flying version of the item, that only hits the first-place driver with an explosion that takes five to ten seconds to recover. By the time the first-place driver is back on track, the second-place driver is likely to have already surpassed him, and usually said second racer is the only one taking any advantage of the weapon. It took Nintendo two more games (Mario Kart DS and Mario Kart Wii) to either realize the mistake themselves or to notice the item's infamy among fans before reverting the item to its non-flying form (while still exploding when hitting the head racer) in Mario Kart 7.
Never Live It Down: Daisy only says "Hi, I'm Daisy" when switching to her and when finishing a race in first place. This is the only game she says the line in. In spite of this, practically anything referencing Daisy online will inevitably bring this line up as if it's her catchphrase.