The car Aidan's grandfather was driving in 1957 had seats from a modern car. Vehicles in the 1950's didn't have headrests.
When Aidan goes to visit his grandma in the nursing home, you can clearly see her "bed" is actually a folding table with a mattress pad on top. Her scenes must have been filmed later after the main production had wrapped, because they had actual beds in the post- crash hospital scenes.
When Aiden is seen going back in time for the first time, he emerges outside Room 41, overlooking himself and Lauren before they go to the diner, where he then causes the crockery to be knocked over. This accident is heard earlier in his pre-time travel conversation with Lauren before she dies, but before that, when they meet in the car park, Aiden is not seen in the balcony above, but he should also have been there then for him to have been in the diner the first time they talk, in order for those plates to have been knocked over.