Continuity mistake: When Sly is in the attic, and the fake power dude comes up to kidnap him, Sly uses a ski to "hit him in the gonads". But if you look closely at his face, the guy who was hit in the nuts wasn't the same guy that fell down the stairs.
Audio problem: Every time Sly laughs, it sounds exactly the same, don't you think they could have recorded more than one laugh?
Revealing mistake: When Sly breaks the board you can tell it was already broken.
Other mistake: When Sly hypnotises the guy, he tells him to wiggle his tongue. He starts wiggling his tongue exactly when Sly says, "Wiggle."
Revealing mistake: When the kid does aerobatics, her uniform is white, and it is an adult pretending. (01:20:25)
Other mistake: In the scene where Sly and Whit are training the other babies, there's a shot of the kids at the nursery school running on the obstacle course that Sly built. He shouts at a kid to go under the net, but is seen running through a part of the obstacle course in the background, and so therefore wouldn't know that the boy is knocking the net down. (01:05:45)