There are many tricks that will help you to skip good portion of course in this game. There are some crazy ones I heard before which some I am yet to confirm. Here are some of them.

Mushroom:
3 (ghost): feather shortcut, can be also used using mushroom (tested)
4 (castle): using the acceleration track from backwards, use a feather, land onto the yellow jumper two turns ahead and land to the goal. <--- This is the craziest one.
5 (mario): The last jump, get onto the left side and land onto the yellow bump right inside the square shaped boundary you cannot get inside to. It will jump you up to the girl. (Tested)

Special
1 (pond): Right after you jump the second broken bridge, use mushroom and jump with L/R. you can jump across boundary you cant usually jump. (tested)
4 (ice): Right before the last turn, you can use mushroom and by using L/R cut straight across the lake. This will save you about 5 seconds. (Tested)

There are more but I am not keen on listing all.

anyone else?

There are loads of tricks. one i remember is putting a banana or a green shell where the zoom thing is on 1 of the levels. the other racers hit them and then dont make it over to the other side and have to go all the way round

The one that sticks in my mind is the one in the Ghost House in Mushroom cup, where you use a feather to jump the little gap. That always use to work for me and was very useful.

quote Henry is king

There are loads of tricks. one i remember is putting a banana or a green shell where the zoom thing is on 1 of the levels. the other racers hit them and then dont make it over to the other side and have to go all the way round

HAHAHAHAHA! Yeah I remember that, too. I did that all the time, I did about 3 or 4 times to 4 different computers in one race and they were all behind. LMAO!