The car that is run off the road and wrecked appears in a later scene, intact and parked on the side of the street in town.
Miss Melanie claims that August 8, 1955 is a Saturday. In actuality, it was a Monday.
Outside the hospital, just before Sam is arrested, Al is stepping on the grass and clearly makes it move, which he shouldn't be able to, being a hologram. (It would have made sense to simply film him standing on the pavement which was close by)
When Sam/Jesse leaves the prison building towards the end, he is reflected in the glass doors. But it is clearly Sam's silhouette, not Jesse's, as it should be.
As hologram Al is trying to convince Miz Melny Trafford not to get in the car, you can see his shadow on the ground and the car door.
When at the cemetery there are mountains seen in the background that are clearly California, not Alabama where the episode is set.
At the end of the episode when Sam is leaving the hospital (while still in Jess's body) the reflection on the door gives away his appearance, it shows Sam's original body on the reflection on the door of the hospital instead of Jess's.