The frog-shaped air purifier in Wyatt and Robbie's room continually disappears and reappears between shots.
(at around 1h 22 mins) Towards the end of the film where the woman rushes towards Alex and Alex slams the door, she is clearly wearing a dark blue top just as the door slams, however as she smashes through the door with the left arm and upper body, she is now wearing a white top ("The woman" is obviously a demon-possessed Katie).
(at around 31 mins) In one scene, Alex follows a trail of toys into Wyatt's room. She inspects his closet and behind her, the toy train turns itself on. Startled, she turns around to head downstairs. On her way out of Wyatt's room the toys are now gone.
When Alex first goes outside into the garden with Ben after her night with her friends, her hair is curly. When she returns it's straight.
(at around 29 mins) After the ball bounces down the stairs Alex goes up to investigate the noise, the ball is still on the stairs. When she comes back down again the ball is nowhere to be seen.
(at around 1 min) At the beginning when Katie takes Hunter away from her sister, you can see Katie's outline standing outside the doorway but she is still downstairs in the lounge room.
(at around 20 mins) When Alex shows Ben the footage from night #1, the Calendar icon in the OSX dock clearly shows a one-digit number (possibly 6, since that's the date it's supposed to be). However, when the shot changes to a closeup, the icon now says it's the 17th.
When Alex crashes backwards through the garage door, we hear the sounds of the car hitting the door before the car even hits it.
Towards the end, Alex is struggling with being stuck in the garage with car exhaust filling the area. All the while it's being recorded on what is most likely an internet connected laptop or cell phone she could have used to call for help. Also all garage door openers have the ability to be manually opened in case of power outage. Possible the 15 year old was unaware of this emergency feature.
(at around 1h 21 mins) During the ending scene, when Alex is looking for her father at an empty bedroom, we can hear a boy (presumably Wyatt) calling his sister 'Kathryn' not 'Alex'.