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.
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.
The movie takes place around 1969-70, yet occasional newer vehicles appear throughout the film. In one of the earlier shots, there is a 1973 full-sized Pontiac parked at the curb. Some 1970s cars are also seen during the film like a 1970 Ford Maverick in the early parts of the movie, a Datsun 240Z, a 1974 Datsun B210 and a 1973 International Harvester Cargostar seen in one of the scenes and lastly, a 1971 Plymouth Satellite seen in the ending scene.
When Mia moves into her new apartment she hears noises from the apartment above her but when Evelyn jumps out of the window with Annabelle you can see that the window she jumps from is the top floor window.
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 it has been taken vertically in a portrait format.
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.
When the priest takes Mia and Leah's photo in the beginning of the movie Leah has her hand in her mouth. At the end of the movie when the priest presents the family the photo Leah is straight faced with her hands at her side.
When John gives Mia the Annabelle doll, Mia goes over to prop her up on a shelf. Watch the black doll on the end of the shelf - her hair moves from behind her shoulders to in front of her shoulders, and then back again, between shots.
When Mia takes the Annabelle doll out of the box in the apartment, John brings in the baby, who has a widow's peak in the center of her forehead. It the next shot, the widow's peak is seen further to the left.
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.