Fossil Canyon: This one is obvious. At the fork in the road, take a left. It's a bit shorter and safer.
Dino Domain Boss: This shortcut is on the boss of Dino Domain (the triceratops). About halfway up the mountain, after the place where you go past a large pillar on the right with two balloons, you should see some bushes on the right. Behind them is a tunnel that will almost assure that you'll win.
Frosty Village 1: In the part where you go past several large pillars, go either left or right off-road. You must make use of the three Zippers of both paths.
Frosty Village 2: You must use the hovercraft to take this shortcut without losing speed. Near the end, you'll see a large outcropping with three ledges on it on the right, surrounded by a lake. Underneath it is a tunnel. Go through it.
Snowball Valley 1: Like Fossil Canyon, take the left path at the fork. It's faster.
Snowball Valley 2: The other shortcut is not really a shortcut. Instead, you must grab one of the shield power-ups before the snowball area. Use it to sail right through the snowballs and gain some ground over your snowball-dodging opponents.
Crescent Island 1: Right before the tunnel at the beginning, you'll see a path on the left. Follow it to get a magnet balloon and get ahead.
Crescent Island 2: Using the hovercraft, go left around the pirate ship to find a shorter tunnel.
Crescent Island 3: Or, you can go on the ship and go on the right path next to the tunnel. Then hop right to go through the hole.
Crescent Island 4: The last shortcut here is found after the pirate ship. On the final turn before the end, make a powerslide/hop right to go around the pillar on the right. It's a great way to win at the last second(and it contains a Silver Coin).
Whale Bay: Use the whale near the beginning to jump over the pirate's ship and get a magnet power-up and jump ahead of you foes. Pirate's Lagoon: Near the end, use the Zipper to jump the ramp and get a Turbo power-up.
Windmill Plains: Go through the windmills at the beginning. Both of them contain a Zipper and a Magnet power-up.
Boulder Canyon: In the area after the indoor waterfall, you will see a red balloon on the left and a green one on the right, leading to the rest of the track. But grab the red one and you'll find a hidden tunnel behind it. It contains two coins and is shorter.
Greenwood Village: Near the beginning, you'll go through a village area. You should see a well. Hit the brakes as you approach it and drive over it. You should fall down to a tunnel with a Zipper in it. This is the shortcut.
Haunted Woods: At the fountain in the village area, take a right. It looks longer, but it gets you to the tunnel a bit faster (and it contains a Silver Coin.)
Sherbet Island Boss/Boulder Canyon: In both of these races, you should gain some speed if you hop over the logs with the hovercraft at the right angle. Be careful, if you go at the wrong angle, you'll crash into the log and lose speed!
Star City: Choose the Airplane, then go into Star City and look for the N64 railway train. Follow it for a shortcut. Note: Do NOT hit the train, or else it will go slower.
Alternatively, continue going straight when your in the glass room. When you exit fly high. Look for the Rareware sign (the letter R) and go right through it.