Visible crew/equipment: When Al, Fonzie, and Howard use "Gulper" in the diner's kitchen, it starts to throw salad all over. You can see the same hand twice in a short period throwing salad from the door window. (00:13:40)
Other mistake: The background action in the opening credits is slightly unsynchronized. This is most obvious at the "Goodbye gray sky, hello blue" line in the theme song, as Potsie mouths the lyrics. It's also obvious at the "My cycle hums" line, as the girl in the blue plaid skirt shows up at "cycle", rather than "my." (01:13:10)
Answer: If all the actors and hands know their roles well enough they could perform the play reasonably well even without a director.
BaconIsMyBFF