Continuity mistake: When we see "Grandpa's Folly" being 'scratched' in his starting box, the box has no door in front of it, but when we see the boxes at the start of the race in the next shot, a door has suddenly appeared.
Continuity mistake: During the poker game, the Colonel says "I've got five aces" and he lies down his cards in front of him. You can see that next to the Colonel there is half a coin and a pack of playing cards. When Bugs says "I've got six aces, sir." he takes the half-coin away from the Colonel, but the Colonel's cards and the pack of playing cards have disappeared.
Continuity mistake: When the coyote is tossing the boomerang up and down, his tail keeps disappearing and re-appearing.
Continuity mistake: When Spike grabs Tom's whiskers and threatens him, the background behind them changes from a fence to blue sky between shots.
Continuity mistake: After Tom has torn up Jerry's diary, you can see that the pie is next the hole of Jerry's home, but when Jerry comes around the corner and sees Tom, the pie is now positioned near Tom's foot.