The rifles carried by Ben and Ralph change. Ben is initially shown shooting at Ralph with a bolt action rifle. Later, he is armed with a Remington pump action. Ralph grabs a tube fed Winchester lever action from the sporting goods store, but when he throws his rifle down, it has changed into a Winchester 1895 with a box magazine.
After Ralph comes ashore in lower Manhattan, amid scenes of him wandering around the vicinity of Wall Street, a shot looking up at him from street level shows the Empire State Building towering above him. The Empire State Building is approximately five miles north of where Ralph had been shown standing.
Sarah states that she survived by staying in a decompression chamber, but that the two men who had entered it with her died because they left the chamber too soon. Since the men had to open the door to the chamber to leave, the radiation would have infiltrated it immediately, meaning Sarah should have died too.
As the three survivors join hands and walk off together at the end, flocks of pigeons suddenly appear. Since the radiation had killed off all life forms that were exposed to the atmosphere, how did any pigeons survive?
While Ralph is being pursued by Ben near the end of the film, he comes to the United Nations complex. Although there is no electric power in the city (except where Ralph has installed a generator), lights can be seen through the windows of the Secretariat tower.
The goof item below may give away important plot points.
Although only 3 people are left alive in New York City after an atomic event, there is not even one dead body. Even an evacuation could not have been this complete in one of the most populated and congested cities in the world.