Bob puts his hand on his wife's shoulder, in the next shot, it is by his side.
When Bob meets Carpenter and Dawson in Salome's for the first time, the first shot when Bob is walking towards the booth show's Dawson's beer glass being at least half full. The next shot when Bob is taking a seat in the booth, Dawson's beer glass is nearly empty. Only a matter of seconds would have passed.
There is a glimpse of the famous Capitol Records building painted silver. At the time of the film, it was actually painted black to resemble a stack of records.
In addition to the Catholic Mass being in Latin, the priest would have had his back to the parishioners, with the altar being at the back wall.
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.
When Crane is heading into his agent's office building early in the film, he passes a blue U.S. Mail box. Mailboxes of this era were red white and blue.
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 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.
In narration, the Bob Crane character says "Hogan's Heroes" was ended after 186 shows. There were actually 168 episodes of "Hogan's Heroes".
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.