When Hilary puts on the 7" single of The Specials 'Do Nothing' the album version plays instead and not the 7" single version.
When Stephen is talking to his mother in their kitchen the day before leaving to study at Bristol (presumably Polytechnic as he uses the word "college" rather than "university"), there is a calendar on the wall that says "July": this is two months too early as the academic year starts in September, not July.
During a scene that takes place in 1981, Janine mentions she heard about a song from SPIN magazine. Spin magazine was not founded until 1985.
First thoughts on watching this film include "When was it set?". A Rover 2000 and a reverse rear windowed Ford Anglia quickly nailed it down to the 60s. Mods, scooters and skinheads later in the film further reinforce these initial thoughts. However, it turns out to be supposedly set in the 80s, as evidenced by the films being shown at the cinema - Blues Brothers, etc. Sam Mendes is British so he would know what he is doing history wise; is this discrepancy deliberate?