Although the American scenes are meant to be set in the 1960s, a lot of 1970-73 cars are clearly seen.
Although the main cast are perfectly groomed and attired for the period in the early-'60s concert scenes, this does not stretch to the extras (the crowd, and in particular the security staff) who are all clearly from 1974. Some of the music also sounds more '70s than '60s.
The "Piano" they play is a Vox Continental organ and this model, single manual with drawbars in the middle and some presets, was only made in 1972-73.
In the first concert scene at the Warehouse Club, set in 1964, the Stray Cats use a WEM public address system, but these were not developed until 1966.