Revealing mistake: During the pirate attack, Rosencrantz sits up in bed, narrowly avoiding a sword that's thrust through the wall next to him. Just before the sword appears, the film jumps a little. It also jumps again just after the sword has been withdrawn and he lies back down. Clearly these two motions (him sitting up and down in bed and the sword appearing/disappearing) are two separate takes that were spliced together.
Continuity mistake: When Rosencrantz and Guildenstern meet the Players on the way to Elsinore, the sky around them changes. In the shots of the players, it's gray sky, possibly approaching dusk, and in the shots of Rosencrantz and Guildenstern, it's pitch black. (00:13:20 - 00:14:40)
Continuity mistake: When Guildenstern tells The Player what he thinks is wrong with Hamlet ("A man talking sense to himself..."), he is holding his hands together in the close-up but not in the wide shot. (01:03:40)