Panic in Year Zero!

When the family is in the car at the beginning of the film and suspect something is happening, they cannot pick up any "CONELRAD" stations on the car's radio. CONELRAD (COntrol of ELectromagnetic RAdiation), established in 1951, was the first nationwide system for emergency broadcasts in the United States. All radios made between 1953 and 1963 were required to have marks on the AM dial at 640 and 1240 MHz where citizens were expected to tune to obtain civil defense information. CONELRAD was succeeded by the Emergency Broadcast System in 1963 (which did not use dedicated frequencies) and it, in turn, was replaced by the Emergency Alert System in 1997.

When the family is trying to cross a busy highway, there are high shots of a four-lane freeway, but in the ground level shots of the family they are clearly standing by a two-lane country road.

Other than the title, all credits are at the end of the movie.