When Jake and Sadie dance in the bungalow, Jake's collar is creased in some shots and straight in others.
When it is determined that Johnny was the one who took the photos of Jake and Sadie at their motel hideaway and slipped them under the door by the next morning, this is 1963 well before 1 hour photo was developed AND even if it had there were no 24 hour businesses open for Johnny to take the photos late on a Friday night and have the film developed and printed onto 8x10 sheets to have them arrive at the lovers doorstep the next morning.
In a scene taking place in late March 1963, you can see that the license plate on Principal Simmons' pickup truck is for 1960 and black with white digits. It should have had a 1963 plate which would have been white with black digits. Moreover, in this time period motorists generally got new plates each year and in Texas the even-numbered years had black plates and the odd-numbered years had white plates. However, none of the vehicles in 1963 scenes have had white plates.
In a scene dated in late March of 1963, Principal Simmons begins a discussion with the high school's quarterback, Jim LaDue, about "his defense." This would imply that Jim is at most a junior and will be playing another season in the fall of 1963. However, when Jake and Bill arrived in the town of Jodie in early November 1960, they passed a weather-worn town welcome sign touting the success of Jim LaDue. If Jim was in 11th grade for the 62-63 season, he would have still been in his first season in 1960 and early November would be prior to him winning his first county championship. Thus, his name shouldn't have been on the sign already unless it was a brand new sign, (which it obviously wasn't).
The red 1958 Plymouth Fury Sadie's husband drives in 1963 has dark tinted windows. Window film wasn't invented until 1966, though this is likely a nod to the infamous Plymouth Fury "Christine" also from Stephen King. In that film, the cars windows were tinted completely black so that you couldn't see who, if anyone, was driving it. In 1958, red was not a paint color option for the Plymouth Fury.
The episode is set in March 1963 but the song "Then He Kissed Me" by The Crystals was not released until July of that year.
You can see the Lavalier mic taped to Bill's chest when he shows Jake the recording of Oswald.