Early in the film, the character of Bob Crane is seen playing the drums in his house. On the underside of both cymbals the large black Zildjian logo is clearly visible. This part of the film takes place in 1964, but the Zildjian company did not put this large logo on the underside of their cymbals until over a decade later. In 1964 they would only have had a manufacturer's stamp on the top and no ink logo. They are clearly modern cymbals.
When Crane's photographs are spread across the floor, we see small black lettering on the back of each print. This black lettering is a computer printout of exposure information, used by photo lab machines only since the 1980s, long after the movie's setting in the late '60s/early '70s.
At John's apartment in 1966, one of the girls asks if he has any records by Procol Harum, whose first album came out in 1967. He then puts on "Helpless" by the Four Tops from their Second Album which was out in 1965. But, the album cover shown is from the "Reach Out" album, which that song wasn't on and which didn't come out until the summer of 1967.
When Crane is being interviewed, the reporter has a Uher 4000 tape recorder on the table. When the reporter starts the interview he only presses one button on the recorder. To record on this model Uher machine, one must press the start and record buttons simultaneously. Also doesn't look like the Power/Speed switch is turned on.
When we see Crane drumming in the strip joint, what he is doing with his drum sticks does not match what we hear in the music audio track. Kinnear also clearly never spent much time practicing on the drum set before filming. Crane was an experienced drummer.
Toward the end of the film, John Carpenter says that everyone's getting into "Betacam". However, that video format was introduced by Sony in 1982 for professional use, four years after Bob Crane's death. What they meant to say was "Betamax", the consumer format, which debuted in 1975.