Continuity mistake: When they are in the lab giving Richie a tour instead of a lesson, they are turning trash into bowling balls as an example. Well, the professor rolls all the balls off and into the container at the end of the ramp, then in the next shot he's holding one which he drops on his foot.
Continuity mistake: When Cadbury burns the prison bars with the "toothpaste", Richie calls his name, and Cadbury looks the opposite way to where Richie is and yells "Richie!" like he'd seen him. Then in the next shot Cadbury is running the right way again.
Continuity mistake: When Ferguson is about to turn Richie and his friends into bedpans, Prof. Keenbean uses the mechanical bee to sting Ferguson. As the camera zooms in on the bee, the glass covering that was removed in the previous shot of the bee is nowhere in sight.
Continuity mistake: When Richie first looks in the mirror thinking he's getting a pimple, he looks at his cheek beside his nose. When he asks his dad if he can see it, he points to his chin.