Revealing mistake: At the point where someone gets a small bruise on the upper arm, the crew are all in a pile and thrashing about on the floor. There are 5 pairs of legs instead of 4. Arthur is in his pajamas, Zaphod is in orange trousers, Trillion is lying on top of Ford and Ford is too far away for them to be his legs. [The fifth pair of legs belong to the person playing zaphod's third arm - doesn't mean it's not a mistake, but that's where they come from.]
Audio problem: When Deep Thought is describing how he's going to create a new computer, he describes it as "a computer that can calculate the answer to the ultimate question." This is wrong: Deep Thought himself just did that. The new computer is supposed to calculate the question, not the answer.