The Barbie doll that can be spotted on the lower part of the screen during the rotating camera sequences throughout the movie is an early 2000s model, making it impossible for it to have stood in a 1988 home as depicted in the movie.
Throughout the film, Kristi carries around a stuffed killer whale. This is actually a stuffed version of Willy from the Free Willy series which was not produced until 1993. It is apparent due to the three black spots on the underside of the stuffed whale's chin. Paranormal Activity 3 is set in 1988 which would make it impossible for this toy to have existed.
While Katie's family are driving to Grandma's house, Dennis turns the camera around and from the back-view of the car, two contemporary cars are seen parked in the background as the family drives past them; because the whole cars can't be made out, the "curved" tops are noticeable.
In the Director's Cut on Night #7, when Dennis goes to get the camera after hearing noises, the time on the camcorder says it's near 3:43am. Albeit in the next shot when he has the camera, the time still says 3:42am (this was probably an error by the editor).
At one point, the family is in front of the house to take a picture of Kristi on her first day of school. This is the photo that was burned in Paranormal Activity 2 and found in Paranormal Activity. In those first two films the girl in the picture is said to be Katie, not Kristi.
The 1980s video equipment room has a road case for modern electronic equipment. One is a CDJ (Compact Disc Jockey) road case. Portable professional CDJ equipment did not exist until the mid-to-late 90s.
While the film takes place in 1988, the home video tapes are presented in wide screen and high-definition quality.
However, this is a necessary and deliberate change on the part of the crew, and not an error.
Producing a movie with "authentic" quality based on the equipment that existed back then would make a horrible quality for it to be seen in theaters and the movie would be unusable to most theaters.
When Julie gets off the phone with her mother to answer the door, the camera begins panning back to the dining room. Just before Julie gets back into view, the dining room chairs' positions, table shadow and the beige couch's change. This is indication that the "Kitchen Drop" scene was performed later on in the day; then CGI stitched together to pull off the illusion that an impossible feat was completed in seconds.
In one scene, where Dennis receives a couple books from Randy (who's also operating the camera); the beginning of the shot shows Randy filming his reflection on one of the TV's; but it's clearly another person filming the shot, the guy's shirt is white and his face doesn't belong to that of Randy.
In the final scene, Dennis is violently back; a lamp is knocked to the ground. The lamp shade (which is on the ground) briefly changes position during a cutaway, when Kristi walks past the camera as her dress briefly conceals the view.
In the second trailer when Kristi can be seen inside of the family's car, the camcorder's time tag shows it reading "PM" rather than "AM", since the scene depicting in the trailer takes place at night.
It is strongly implied in the first two films a house fire occurs back in Katie and Kris ti's childhood; albeit it never happens in this film. (The scene was shot but was cut out, although you can see the parents' bed on fire in the end during the static)