(at around 38 mins) When Father Perez takes Mia and Leah's photo, he is holding the camera horizontally at a landscape angle, however, when he presents the photo to Mia at the end of the film (at around 1h 30 mins) it has been taken vertically in a portrait format.
(at around 38 mins) When Mia is talking to the priest after he takes her photograph, baby Leah is wearing a bonnet, which then disappears and then reappears between shots.
(at around 27 mins) When John brings Mia food home, she chooses the jars of pickles and French mustard, both closed. She then opens the jar of pickles, but not that of the French mustard. The shot immediately following this shows her dipping the pickles into the mustard.
(at around 51 mins) When Mia and John are taking to the priest in his office, Mia is fiddling with the small statue on his desk and faces it towards herself, and in the next shot it is facing the priest.
(at around 53 mins) Prior to Mia going into the basement, she is wearing dark green pants with a white shirt, but while in the basement she has beige pants with the white shirt.
(at around 1h 23 mins) The voice heard from the record was backwards, but the record was playing in "normal rotation" (clockwise).
(at around 48 mins) In the dinner scene where Mia is waiting for John to come home. After she turns off the record player but just before it turns itself on again, you can see blurry reflection in the picture of the person turning on the record player. But this was supposed to be visible, because it was a manifestation of the haunting.
(at around 56 mins) Mia's apartment has an upstairs neighbor, so she is not on the top level of the building. But when Mia is chased into the elevator, she presses what seems to be the top most floor's button, number 6. Actually, there's a number 7 button right next to it.
(at around 32 mins) When Mia cuts her finger sewing, she rinses her finger in the bathroom where she turns on an obviously modern faucet.
(at around 33 mins) After the kitchen fire, Mia tries to run but falls and is dragged, when she stands up her (fake pregnancy) belly is shifted to the side.
Leah doesn't age from the time she's born. When she is first seen after her birth, she looks around 6 months old. 6 months later she is the same age.
(at around 15 mins) 911, while invented in 1968, did not become a nationally recognized emergency number in the US until the '70s and '80s. CA, where the movie was filmed, had universal 911 for all counties in 1985.
(at around 34 mins) When Mia gives birth to her daughter, she is hooked up to a modern IV kit where the fluid is contained in clear plastic bag. A glass bottle, not a plastic bag, would have been used until the early-1980s.
(at around 19 mins) Even though the clinical use of Ultrasound was perfected by the end of the 1950s, it didn't really take off in British hospitals until the 1970s, and it was well into the 1970s before it became widely used in American hospitals.
After the attack on their neighbors, Mia calls 911 and asks for an ambulance. She is shown being treated by paramedics, which did not exist at the time as the ambulance's sole purpose was just to transport the injured to a doctor or hospital. Usually, medical emergencies were handled to by police and/or fireman, even if they had no formal medical training. Since the film takes place in 1967, the first paramedic program in the United States was inaugurated until the year after and even then, it was only in New York City at Saint Vincent's Hospital. The Los Angeles area did not have a paramedic unit until 1972, eventually becoming widely accepted and used across the United States in the early 1980s. Oddly enough, a lot of doctors and nurses didn't see the value in training medics to perform first aid and/or life saving medical procedures outside of a hospital, but statistics from the first paramedic pilot programs could not be argued with as a percentage of patients that survived the trip to the hospital with paramedics present was dramatically higher.
(at around 32 mins) When the popcorn is popping on the stove, it makes no sound.