Modern cars can be seen throughout the film.
Items in the film (i.e., cans and bags) have barcode symbols, which didn't exist in the 1950s.
At the beginning of the movie, when the mother is making breakfast, a Crock Pot can be seen on a shelf. Crock Pots were not invented until 1971.
Near the end when the family is stopped at a railroad crossing, the caboose on the train is Burlington Northern, which wasn't formed until 1971.
The Reward poster for Fuzzhead shows an all-digit phone number. In the 1950's, all phone numbers had a two-letter exchange name, followed by 5 numbers.
The story takes place in Indiana, but Texas license plates can be seen on many of the cars.