At the first murder scene, the shotgun is a different model outside the house and inside the house.
When Mike Anderson is riding in his van around dusk en route to the scene of the first murder, his beard has reached an obvious black stubble stage. A few hours later in the plot, he is clean shaven. His activities are all accounted for over this time period, and taking time out to shave was not one of them.
When Andre Linoge has Joanna levitated holding candles, they're dripping wax on her hands. When he releases her and she embraces Mike, her hands are clean.
When they are trying to bring Linoge in through the back of the store, Alton Hatcher say's he unlocked the door. But when Robbie Beals tries pulling on the door, you can clearly see the lock is still engaged.
When Pippa has her head stuck between the posts, the amount of the red jelly on her mouth changes between shots.
In episode 2 and 3, Linoge mentions the disappearance of the colonists from the village of Roanoke, Virginia. In actuality, this happened on Roanoke Island, off the coast of North Carolina.
When Cora Stanhope is washing up in the town hall ladies lavatory, just as Linoge is mimicking her movements in the jail cell, the left hand sink tap is profusely leaking from the tap handle.