Revealing mistake: When Mr. Kubitz arrives at the house and finds Phil with makeup on, a car is driving by in the background. A few seconds go by before the shot goes back to Mr. Kubitz - plenty of time for the car to have driven out of shot. But when Mr. Kubitz is shown at the doorway again, the car is still there, driving along.
Continuity mistake: When they are first signing up people for the daycare, they get to the little girl with all the allergies. As the girl and her mother are listing all her allergies, Eddie Murphy has his hands by his chin not writing down anything, in the next shot he suddenly has a pen in his hand.
Continuity mistake: When Charlie and his son are sitting at the table having breakfast, Charlie puts his fist to the side of his face, and his son copies. In the shot of both of them, his son's hand isn't a complete fist, he still has his fingers pointing out, but in the next shot of just him, his hand is a complete fist.
Plot hole: It's amazing that the two Chapman women weren't caught at "Rock for Daddy Day Care". One of them unzips a guy's dog costume in the middle of the path with everyone walking by. A little kid actually stares right at her when she does this. Also when Jenny puts the cockroaches in the salad, the people who were waiting in line for food would definitely have seen her. There are many more parts like this.