Continuity mistake: When Sawyer is put back in his cage after being given a pacemaker, he dips the sponge in the bucket straight away. As soon as the shot begins when Sawyer is looking at Kate undress, he is holding a completely dry sponge in his hand.
Plot hole: When Zach first talks to Amy, he advises her not to use the excuse "I work here". But Zach was still walking over to her when she said that, so there's no way he could have known she said it.
Audio problem: When Lister says "he was in sickbay for a week", once the shot changes we once again hear him say "for a week". Evidently, the line was intended to carry on into the next shot but wasn't edited out.
Trivia: The Cornetto joke originated when Edgar Wright (the director) got extremely drunk as a teen and somehow had his hangover cured in the morning when he ate a Cornetto. The reference in this film is made when Ed asks for a Cornetto while he has a hangover.
Other mistake: When Joe falls on the bungie, we see him hit his head in an entirely vertical position with his head at the top. This could not have been achieved considering the position he was in in the shot before.
Other mistake: When Marcus is knocked out at the library, look at his legs when he is dragged away - they are purposely crossed in a way which couldn't have happened naturally for a body being dragged - the actor did it to keep himself comfortable.