Revealing mistake: On night 21 the time-stamp changes from 11:59:56 PM to 11:59:57 AM despite it not having turned midnight yet.
Visible crew/equipment: When Mika brings Katie upstairs after investigating another noise downstairs, you hear a thump come from downstairs. Mika turns the camera down the stairs, and you can see a crew member scrambling to get out of the shot.
Continuity mistake: On the first night the girl is wearing pink night shorts, when they wake up in the morning downstairs she is wearing blue.
Continuity mistake: During the demonologist come in, he closes the gate and door. After the meeting, he open the door but the gate is open.
Revealing mistake: In most of the shots with fast forwarding you can see that there is no synchronization between breathing movement of the stomach and the time passing by (most obvious on night #15 when Katie is standing looking at Micah who's still asleep). (00:37:50)
Other mistake: When Katie tells Micah to look at their picture after the demon has broken the glass, you can plainly see the girl in the picture is not Katie.
Suggested correction: Yes, it is. She looks a little different in the picture, but it just comes down to the camera angle (it's a high angle) and the weird lighting in the photo (she's in shadow). I also checked out a high-resolution still of the photo in the movie and compared it to a photo of the actress, and they share every minor subtle feature right down to the shape of her teeth. Micah also looks slightly different in the photo too, but it's the same actor. Also, I have to ask what purpose would there be to having a photo with a completely different actress when they could just take one with the actress from the movie?
Other mistake: Katie is supposedly a student, but she hangs around the house all day and doesn't go to school. And Micah never once leaves the house to go to work, which again he's not set up to do remotely.