Continuity mistake: When they're demonstrating the LAW rocket, Callahan's new female partner is standing behind the instructor. He pulls her away before the rocket fires. The angle cuts, and she's back closer to the instructor again. If she was standing where she was the second time, she would've been hit by the exhaust (which is why he pulls her away).
Revealing mistake: A crowd of people are watching the filming as Harry sprays one of the kidnappers with a water hose. (01:25:49)