In the beginning of the movie a character is seen using a "brick" mobile phone. The first mobile phone (the Motorola DynaTAC 8000X) was brought on the market in 1983 and therefore such a phone couldn't be in use in 1981.
Within the first few minutes of the film, a second generation Honda Prelude is seen passing in the street. In 1981 when the film takes place, the Prelude was still in the first generation (1979 - 1982).
When John picks up Dawn at Sally Hansen's house, she has with her the little dog, but when they leave running down the stairs, she has nothing in her hands, while he has a briefcase. Then, when they are in the car, Dawn has the puppy back with her.
When John picks up Dawn at Sally Hansen's they have sex in the bathroom. As they begin John pulls down Dawn's shorts and underwear. When Sally bursts in, they are still having sex, but Dawn's underwear is now back on.
John drives a blue Chevrolet Chevelle. However, the year of the car changes from scene to scene. When picks Dawn up from Sally Hansen's home, when he drives away, you see the car has round tail lights, characteristic of a 1971 model. In the scene when he drives to see Eddie Nash, the car has the square tail lights of a 1972 model.
When Ron is enraged with John, while at Wonderland, he picks up some sort of entertainment component (VCR, Cassette Player, etc...) and throws it through the picture window which crashes into the street below. Not only were there no cables attached to the component but the picture window was actually showing shatter marks before it flew into pieces when being hit by the component.