In this game's TV commercial, when Princess Peach throws a Banana Peel in front of Donkey Kong Jr. who's catching up to her, she is using her left hand. In the next shot, when Donkey Kong Jr. hits the Banana Peel and spins out, Peach has her right hand extended out instead before retracting it back on the steering wheel.
In the game's manual, the karts are incorrectly spelled as "carts" when referring to the remaining number of karts after the player finishes a grand prix race in 5th - 8th place and must retry.
In international versions outside of Japan, Princess Peach is referred to as "(the) Princess" with no mention of the fact that another princess by the name of Princess Daisy already exists in the series, having debuted in Super Mario Land released three years prior. So technically, two princesses already existed in the entire franchise from that time period before this game was even considered while only including the former of the two in this game.
Lakitu's artwork depicts him holding the fishing pole with starting lights in his right hand. In the game, he holds it in his left hand.