Visible crew/equipment: As Klink's car pulls up, and Klink comes around the front of it, the shadow of the camera is visible.
Revealing mistake: After the cell door blows, you can see the fuse of the stick of "dynamite" Newkirk placed still burning on the ground. Since the dynamite would blow when the fuse is burnt up, that literally can't happen. (00:22:40)
Answer: It's a comedy, not a documentary.
stiiggy
Perhaps it was counterfeit. There are numerous episodes where they deal in counterfeit monies.