It might seem strange at first in 7 when racing underwater doesn't clear away Blooper's ink, until you realize that as an aquatic life-form, Blooper would have little use for water-soluble ink.
Some kart bodies give a speed boost in the air or underwater. Some are obvious, like the Soda Jet in the air or the Tiny Tug in the sea. It may seem odd that the Pipe Frame gives an underwater speed boost, but remember that water usually travels through pipes.
7's gold tires and gold kart give a boost in weight when used due to how dense gold is in real life.
The Egg 1 in 7 offers a huge underwater speed boost due to eggs and osmosis.
It may be a bit unusual at first for an Arabian theme stage to deal with Shy Guys, but it has shout-outs to Super Mario Bros. 2, which was originally called Doki Doki Panic, which itself was an Arabian themed game. (And also the first true appearance of the Shy Guys)
Why is Waluigi Pinball in 7 despite Waluigi not being in the game? To make up for not being able to play on Waluigi Pinball online in Mario Kart DS!
The box art for◊ 8 is apparently referencing Super Mario 3D World. You have the six main characters: Mario, Luigi, Peach, Toad, and Rosalina, the playable characters, and Bowser, the main antagonist.
From DS onward, every Mario Kart has had 32 courses. The same as the number of levels in Super Mario Bros. 1, and in the same arrangement (8 cups\worlds with 4 levels each). Granted, it could be unintentional, but still.
Mario Kart 8's Rainbow Road threw many for a loop. Think of it this way, though. The retro Rainbow Road has a mystical, enchanted, magical aesthetic to it. What's the logical way to differentiate a new Rainbow Road from that? Make it a constructed, man-made, spectator track.
Baby Rosalina's introduced in Mario Kart 8. Confusion arises because Rosalina's implied to be canonically thousands of years old in the past games. However, who says that the time travel method that were used to bring the other baby characters to the present can't go that far out into the past, and that Baby Rosalina can't be taught to drive a go-kart/bike despite both probably not appearing at that place in time?
Metal Mario's animations are different from the real Mario's by how stiff and sort of robotic they are. In contrast, Pink Gold Peach has animations that are much more fluid than the real Peach's.
Whenever Koopa Troopa is a playable character. The Koopa still has a chance to get a shell, think about it for a second...
Granted, by the time the first Mario Kart game came out, it had already been established in Super Mario World that, unlike real turtles, Koopa shells are detachable and their owners can survive without them. Though that still doesn't answer where all those empty shells come from...
You can throw/set Bob-ombs in Sunshine Airport in 8. That's right. You can use explosives in an airport.
Well, you could also use explosives in Coconut Mall, so ...
So you're racing, and after taking a break and going to the fridge for a soda/water/what-have-you, you pause and realize that there were babies in the race. Babies whom the other characters (even Mario!) are just as willing to hurl bullets, shells, and even bombs at as they are the adult racers.