During the scene where Scott is getting ready for his ceremony, his collar is up. When Brenda goes over to him, she flattens only one side of his collar, however in the next scene, Scott's collar changes.
When Scott and Adriana are in the confessional booth drinking, Adriana takes her first sip of the wine from the bottle, and passes it through to Scott neck first, but when Scott receives it, he's receiving it bottom end first.
Historically, the Iranian Hostage Crisis and the Falklands War happened two years apart, not in the same year as the movie depicts.
The Falklands War happened in 1982 (after the setting of the movie in the late '70s) and was fought between Great Britain and Argentina. It did not involve any American troops.
Though the movie is set in the 70s, when Scott is in his room, pretending to be Han Solo, he says "Some friend you are, Lando". Lando Calrissian did not appear in the Star Wars movies until The Empire Strike Back, which came out in 1980.
The movie is set in 1979 - 1980 but modern vehicles can be seen in the background when Adrianna and Scott walk along the railroad tracks.
There's a shot of a Lego model of the Space Shuttle Discovery, which didn't actually launch until 1984. Lego didn't release a Space Shuttle model of any kind until 1990.
Towards the end, the school bus that comes to pick up Scott and Adrianna is a Navistar 3800 model which was not introduced until 1989. In fact, Navistar wasn't even a company name until 1986. In the 1970's, that company would have been known as International Harvester.
In the transitional shot from the scene where Scott's mother attempts to force him to apologize to a boy he just beat up, a passing train is visible in the background. Though the story is supposed to take place in Long Island, the train is distinctively a NJ Transit train, not a Long Island RR train.
On the sign announcing the construction of the Bartletts' new house, the Bartlett Group's address is given as "329 Empire Road, Long Island, NY, 89023." It is more likely that the town would be given (e.g., "Bethpage, NY" rather than "Long Island, NY"), but in any case 89023 is a Nevada zip code.