I haven't found very many shortcuts but at least I've found 4.

The first one is in Koopa Troopa Beach. After you go under the arch there are three ramps. After the ramps there is a smaller ramp next to a palm tree. Go straight up the middle into the hole in the rock.
The second one is in Yoshi Valley. When you see a sign point off the road just follow it!!!

The third one is in Rainbow Road. At the beginning there is a steep hill .When you start to go down it hold down the jump button and make a sharp turn to the left (to the right in extra mode) and you will land on another road. This takes a lot of practice.

The fourth one is in DK's Jungle Parkway.At the begining turn around and then go into the cave and then turn around again and angle a little bit to the left and run into the side of the wall. If you do it correctly lakutu will put you back in the cave and then go forward to the finish line to advance a lap!!!(see page 93 of vol. 98 of Nintendo Power)

I have these games.