Visible crew/equipment: At Barbara and Phil's house, just as the hooded zombie bites a chunk out of Phil's neck (before Shaun leaps over the car hood) the black mat with two long white marks is visible on the pavement, behind the second zombie (beside the car). It's gone in following shots.
Continuity mistake: When Shaun goes to the newsagents after the dead rise, he gets a drink out of the fridge, which has blood-stained hand prints on. He slips on what we assume is blood as he walks away, yet on the way in and as he leaves the shop you can see behind him that there is no blood or any other liquid on the floor.
Revealing mistake: In the beginning of the movie, where it shows the group of nodding zombies and the Shaun of The Dead logo is on the ground, look to your left, the zombie actor stops nodding and looks around him to see if the shot is still being filmed, and he immediately goes back to nodding. Look out for it, it's obvious.
Continuity mistake: After Ed and Shaun make the plan to save everyone, we see the close-up shot of the TV where the announcer is saying that nobody should try and save their friends and family. If you look at Shaun, you see the handle end of the cricket bat in his right hand, and he is facing the TV screen. In the shots immediately before and after that, Shaun is not only turned away from the TV, but the handle is in his left hand.