Dana's motel room has a door with a lock requiring a magnetic stripe key card. While the magnetic stripe concept has existed since 1960, it would be extremely unlikely to see a motel with such a lock before the late-1990's.
After Norma's Father runs Arlington's license plate number, he refers to the vehicle as a "Town Car" but Lincoln did not come out with the "Town Car" until 1981. Up until then, and in the year this movie takes place, the use of "Town Car" was only used to denote a trim package on the Lincoln Continental. Someone referring to a Lincoln in 1976 as a "Town Car" would make no sense. It would be like describing a car as "sport package" or telling someone "It was a Ford 'Luxury Edition'".
When Norma's watching television early in the film, a commercial comes on advertising the debut of the sitcom "What's Happening!!" The date was earlier established as December 16, 1976, when Arthur attends the Viking seminar. "What's Happening!!" actually premiered on August 5, 1976.
During the NASA presentation near the start of the film, the projected image from behind the speaker is visibly pixelated. This would only happen with a digital projector, which didn't exist in the 1970s.
The license plates show 7 characters. In Virginia, in 1976, the auto license plates had larger letters/numbers & were always 3 letters with 3 numbers, also with a month sticker on the upper left with the year sticker in the upper right of the plate. Some of the cars in this movie show 7 number/letter combinations in a smaller "font" and with only a year sticker.
When Walter and his 'nanny' decide to go down the basement, he allows her to go in and down the stairs first. In the next scene, when they have come down the stairs and into the basement, he is seen coming down those stairs first and his 'nanny' follows.
The stop for Santa standing in the middle of the road ringing a bell. Santa is brightly illuminated by their headlights. After the truck hits them they go back to Santa, still ringing the bell and still illuminated by their headlights.
When being followed down through the corridors of the library, they enter a main hallway where it shows his followers coming from two different directions. Yet just a second before all five of them were coming from the same direction as he was.
Around 33 minutes into the film when Arthur goes to unplug the Christmas tree he bends down next to a window. Just then a man's head starts to rise from the outside into view of the window. You can only see the top half of his head and it lasts for about a second, so its not part of the film. It's just out of place.
The protagonist's disappointment in not being elected for the astronaut program makes little sense as the MAJORITY of people who applied (and who apply) for the program are rejected. In fact, he should have been more surprised that he had been chosen than that he was not. It's unlikely that he would have been "depending" upon the selection for his future as the odds of being selected would be so remote.