The vase of flowers on the dining table downstairs disappears and reappears randomly throughout the movie.
(at around 31 mins) 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).
The bank-and-forth movement of an oscillating fan, especially the style shown for use on the downstairs camera, is created by gearing at the back of the fan's motor. By removing the fan and motor, it would no longer oscillate.
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.
(at around 1h 4 mins) While driving the Mercedes to the house of grandma, the gauges on the dashboard clearly show that the speed is zero and the engine is cold.
(at around 1h 3 mins) 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 couches change. This is indication that the "Kitchen Drop" scene was performed later on in the day; then editing was stitched together to pull off the illusion that an impossible feat was completed in seconds. You can vaguely see the fade transition as Julie walks back toward the kitchen.
(at around 32 mins) When 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.
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.
(at around 22 mins) Dennis gave Kristi and Katie some M&Ms the night they slept outside in the tent. One of the girls ate a blue M&M. This movie was set in 1988, but blue M&Ms weren't introduced until 1995.
(at around 13 mins) In the film Julie talks about Virgin Mary on a slice of toast, this famously happened in the late 1990's.
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.
(at around 26 mins) 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 Dennis is editing one of the video tapes, there's one on a table labeled "89" even though the film takes place in 1988.
(at around 18 mins) When Dennis is talking to Kristi after watching the first night's tape, she says, "He's my friend," but it doesn't match the movement of her lips.
(at around 56 mins) Its shadow can be seen on Randy's back as Dennis follows him (with the camera) to the garage, after the Bloody Mary scene.