I just thought of another one, from Star Trek V: The Final Frontier, specifically the infamous "turbolift shaft" sequence in which Spock uses rocket boots to give Kirk and McCoy a "lift" to the upper decks. Actually, this sequence has a number of mistakes:
1. Visual Error - On the turbolift shaft wall you can see the shadow of the support bar that was holding Nimoy.
2. Continuity - When Kirk and McCoy "climb onto" Spock, they each place one foot on one of the rocket boots, but subsequent shots show their feet dangling.
3. Continuity - As the three of them rocket upwards, the deck numbers are out of sequence as they "fly" past: Decks 35 and 36, Deck 52, Decks 63 and 64, Decks 63 and 64 (again) and 65, Deck 52 (again), Decks 77 and 78, and Deck 78 again before reaching the top of the shaft. To further complicate matters, the Enterprise (NCC-1701-A) allegedly has only 21 decks.
4. Continuity/Factual Error - The deck numbers get larger as they fly upwards. The bridge, which is on the top of the ship, is on Deck 1, so the deck numbers should get smaller as they move upwards.