In the section right before the cave on GCN Sherbet Land, there are two Shy Guys skating together and doing tricks. It's a small, but sweet sight to behold.
The characters' laughter/cheers when performing tricks and such can be this, depending on the character. It's nice to hear Rosalina sound so upbeat after all her years of loneliness in space. Hell, just look at Link! The guy is excited to be in the race, and it's nice to see him having some fun for once.
The sight of some of these retro tracks not only being imported into a new Mario Kart game, but getting an unprecedented graphics overhaul to the point where they look totally brand new when paired up at their less graphically advanced original designs. Some veteran fans may have imagined these tracks with better visuals, but to take it the extra mile and throw in Scenery Porn that was not even in the original shows the game designers truly pulled out the stops on this one.
Koopa Troopas are guiding the trolleys in Toad Harbor. It's really cute seeing the normally antagonistic Koopas giving cheerful Toads a ride around the bay.
Koopa Troopas and Shy Guys dancing together in Electrodrome, with Larry as the disc-jockey.
The general sense of togetherness and happiness that the game portrays with the cooperative and pack mentality friendly collision boost mechanics of the zero gravity sections and the celebratory and party atmosphere that's prevalent in a lot of the tracks is very heartwarming indeed. It's as if the game is a gigantic party celebrating Mario Kart's history and future in-universe.
In multiple courses, the crowd will go absolutely wild when you pull off tricks. It's bound to make anyone smile.
The love that Nintendo has been giving to third-parties in Super Smash Bros. has spilled over into Mario Kart, where racing suits of Sonic, Mega Man, and Pac-Man are accessible.