Factual error: We see Jamie at his karate graduation as a yellow belt. In the scene where his dad apologizes for missing it, he picks up Jamie's new belt, which is purple. Although the order of belt ranks varies by discipline and by dojo, it is highly unlikely that any sensei would have yellow belt (which is almost always the second level) followed by purple (sometimes as low as the fourth ranking, but more often up to the seventh or eighth rank).
Continuity mistake: In the scene where Arnold trips up Sinbad with a remote control car, as he slips upwards the car comes to a halt. We see a brief shot of Sinbad on his back after he's landed - the car has vanished. His post bag is also closed, and there's nothing on top of him. But in the next shot where Arnold runs past and says 'Aww Poor baby', he is covered in letters. (00:20:35)
Other mistake: When Howard is running behind the car driven by the lady in the fur coat, he's always shown directly behind the center of the car, but when the lady looks in her side mirror (from her point of view), Howard is in the center of the mirror. In reality, she would only see a part of Howard's left side in the reflection (not his whole body).
Continuity mistake: When turbo man takes of his helmet at the end, his head gear has completely changed, he is no longer wearing the pink neck collar or head covering, or the bits that cover his ears that match his costume, he is wearing a normal helmet.
Revealing mistake: When Howard arrives at the Mall of America he comes down an escalator. We then see a shot of the gathering crowd in front of him. In this shot you can see Howard with a woman in light blue with her hand on his left shoulder as he pushes his way through the crowd. This is before he joins the crowd. (00:26:10)