Visible crew/equipment: When Calvin is getting pulled up the hill by his dog. He is still on his skateboard and going up a grass hill. You can totally tell he is riding on much bigger wheels than he was before. Therefore the wheels need to be bigger so they can go up the hill.
Revealing mistake: When they are playing N64 look at the system, there is no game in it.
Continuity mistake: When Calvin is doing his skate trick in the dog show, when he goes on a ramp, it breaks and he flies his arms and legs are moving between shots.
Other mistake: In the beginning when Tyco is a puppy, it is raining but the blanket that is in the box is still dry.