When the gang first descends into the sewer all of the men are standing in waist-deep water. During the confusion, Harry Lucas falls into the water to his neck, but in the next shot is suit jacket is dry. A few minutes later the gang is seen ascending the stairs and all of their clothes are completely dry.
When Avery is being shown the second hearing aid, Luther leans forward and puts the single earpiece into Avery's left ear. In the next shot, Luther is again leaning forward with the earpiece, yet it never makes it up to Avery's ear.
Shortly after entering the printing room, Luther is seen standing with a box in his left hand, the open flaps of which are on the left side of the box, pointing away from Luther's body. Immediately n the next shot, the open flaps are on the top of the box, pointing up. This is followed immediately back to a shot where the open flaps are once again on the left side.
The title refers to the US Mint; however the mint only manufactures coins. Bills are printed by the Bureau of Engraving and Printing which is a completely separate agency.
The sewer trap door at the bottom of the print factory is actually a studio prop used for submarine hatches. The extreme arch tops were designed to withstand immense underwater pressure, not to seal off a basement manhole.
When the Captain arrives in the sewer system with the replacement boats, he's shown riding in a miniature tugboat pulling five additional small boats. However when leaving with his 'crew', there are now seven filled boats, one each for Harry, Verna, Luther, Ralph, Dugan, Pop Gillis, and beagle Inky with her newborn pups.
When the team discuss printing $50k, they say it will take 30 seconds. That means 10 minutes per million. When they're in the printing room the guard leaves and Harry says they have one hour. However they have to print $8 million and get the safe open first. It can't be done in time even without the other delays.