Early in the film, Brian is shown being driven on a highway in the back seat of a car. Out the rear window, one can clearly see a 2nd generation Toyota Prius. These were not produced until 2003, with even the 1st generation unavailable until 2000.
The quiz teams are shown answering questions in 2 picture rounds, but in 1985 there was only 1 picture round and 1 music round in each episode of University Challenge. The 2 picture round format is a recent innovation.
The film is set in late 1985 and early 1986. The students drive to the University Challenge recording in Manchester in a Citroen 2CV car with a tax disc that expires 12/1985. However, the car itself has a "D" registration suffix, which dates the car to 1 August 1986 at the earliest.
During the 'University Challenge' competition, Brian answers a question with "Calcium Sulphite" and the question-master says he gave the correct answer of "Calcium Sulphate" (a different compound). An alternative interpretation is that because Brian comes from Essex, he would pronounce "sulphate" like "sulphite".
The producers of this film may have dug a pit for themselves by choosing to set it in 1985. The 1985 competition (which was not broadcast for a year) was a brief return for the series after a short hiatus. Granada had decided to pep it up by modifying the format. In round 1 teams played each other over two programs, the first of which comprised of a "baton relay". Competitors were pitched one-against-one and had to answer two questions correctly before passing the baton on to the team-mate to the left. None of this was reflected in the film. In addition, the set was completely redesigned in red and black, unlike the more recognizable scheme employed in the film.
In the follow-up questions on University Challenge, answers must be given through the team captain. The movie shows both Alice and Brian answering follow-up questions themselves. However, this was quite normal in the original series, the "captain restriction" appearing to be a feature of the Paxman era.