Factual error: The police vans used in the riot scene are Austin-Morris J4 models, with B registrations, dating them to 1964. The Austin-Morris badge on the front of these vans was only fitted to vans made between 1971-1975. If it is a 1964 van the badge on the front should read Morris Commercial.
Factual error: This error occurs throughout the film, but is most noticeable in the sequence where the mods have arrived at Brighton, and Jimmy & Steph are walking along with the scooters parked behind them. One can see Lambretta models that are yet to be produced. There is an abundance of SX and GP models. SX's were not produced until 1966 and GP's were not seen until 1969. Look carefully and one can see an Indian produced GP that didn't reach the UK until 1970.
Factual error: During the party scene, as Jimmy changes the record that's playing to My Generation, a copy of The Who Sell Out can be seen in the background. This LP wasn't released until 2 years after Quadrophenia was set, in 1967. The actual version shown is an early 1970s re-issue, so it's actually around 10 years too early.