Continuity mistake: Halfway through the show, they get caught not having the boat, and McHale gets taken by boat to the commander's office. As he leaves the pier, he drops the rope on the seat next to him, they do a close-up and the rope is behind him about 5 feet away.
Dear Diary - S2-E23
Continuity mistake: After the Captain and Parker land on an island and get out from under the parachute, the Captain's stripes on his left shoulder are hanging loose. The very next cut, the stripes are back on properly.
Visible crew/equipment: 2/3rds into the show, in Binghamton's office, Ensign Parker is making believe he is a Royal Navy Admiral and McHale introduces himself. The camera zooms in and the shadow of the equipment goes across Binghamton. He even looks at it but goes on with the scene.