Other mistake: The scene in Klink's quarters is one of a few where you can see Larry Hovis' (Carter) wedding ring.
Continuity mistake: After Hogan, LeBeau, and Newkirk leave, Carter is sitting, holding the glass with both hands. After the cut, he's holding the glass in his right hand only.
Visible crew/equipment: After Hogan goes down into the tunnel in Klink's quarters, the stove moves back in place. As it does, the wire on the floor pulling the stove back in place is visible.
Answer: It's a comedy, not a documentary.
stiiggy
Perhaps it was counterfeit. There are numerous episodes where they deal in counterfeit monies.