In episode 7 Jake and Sadie steal a car, and Jake says 'I'll hot-wire it' which he then does. However when this scene is shown as a recap at the beginning of episode 8 Jake says 'I'll jump start it'.

The main premise of the show is that the protagonists don't know for sure that Oswald was the lone gunman hence the long stakeout. However, given that going back 'resets' everything the quickest way to ascertain Oswald's involvement would be to shoot Oswald, go back to 2016 and see if Kennedy survived. If he was still assassinated then going back again would 'undo' Oswald's unnecessary death and Jake could concentrate on finding the real assassin.

But Oswald only returns to the US in 62. So it will always take at least 2 years to complete the test.

Highways are shown with modern yellow lines and markings. Prior to 1971 US highway lines were white.

By the early 1960s, the majority of cars/trucks of the 1940s, and even early 1950s, would not have been in such pristine condition. This observation applies to each episode.