Factual error: When Klaus and Ben visit Dave at the hardware store in November 1963, they arrive in a 1965 Imperial. (00:32:48)
Continuity mistake: When Carl is shot and falls to the ground, the position of his body changes. For example, his left arm is down, but in the wide shot, both arms are straight out in a more dramatic pose.
Factual error: Ray comments on how Diego 'beams' into his living room. That use of the term comes from the 'Star Trek' TV series, which wouldn't debut for three more years.
Factual error: JFK was assassinated on 22 November 1963. However, when #5 fights his older self in the parking lot, you can see what appears to be a 1965 Pontiac GTO. The car shouldn't exist for two more years. (Best view is when Luther starts reacting to having been kicked in the testicles by young #5). (00:15:21 - 00:16:36)
Continuity mistake: When the siblings are in the elevator, leaving the meeting with their father, they have fruit on them from the demonstration of Vanya's powers. Alison has some fruit in her hair in one shot; the next shot the fruit is gone; then it's back.
Factual error: As the camera pans towards the interstate after the assassination of President Kennedy the Dallas County court house and part of the county jail can be seen. Both buildings weren't built until the 1980s.