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.
When Ralph exits the mine, his previously soaking-wet clothing is completely dry.
The books on the shelf behind the bed Ben is in change order between shots.
Ralph throws the mannequin from his apartment, and its leg is at least three feet from the curb. When he gets down to the street, the mannequin's foot is on the curb.
Early in the film, Belafonte stands over a table where a newspaper has a huge headline saying "ALL HOPE GONE SAYS PRESIDENT." Then the camera switches to a tighter, subjective shot and now the paper says "U.N. RETALIATES FOR USE OF ATOMIC POISON" with a secondary headline saying "World Doomed, States Dying President."
Someone says over the radio that the radioactive poison was an isotope of sodium with a half-life of 53 hours. There is no isotope of sodium with that half-life.
Although only three 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. This is also noticeable in the empty turned-over buses and the fact that there is not even a dead dog or cat to be seen. However, on the tape at the radio station, the radio announcer says that New York had been completely evacuated so there wouldn't be any bodies.
In his kitchen, Ralph shows Sarah how he's been throwing his dirty dishes out his apartment window because there's no water to wash them with. Sarah simply turns on the faucet and water flows, thanks to the water tower on top of Ralph's building. Ralph should not have been surprised by this, as he should have noticed that his toilet was still working. In addition, both they and their hair look spotlessly clean, with Sarah's hair being particularly shiny.
However, as he explains, he took it for granted that the water system in the building did not work and there is no mention of whether he had attempted to flush the toilet. Also both people had access to water, soap and shampoo so they would be able to keep themselves clean.
After Ralph telephones Sarah, he tells her to turn on her radio. When she does, Ralph's voice is heard coming through. This occurs without him telling her the frequency he is transmitting on or her adjusting the radio's tuner. However, since he had been working at her home, he could have turned the radio to the appropriate station in advance.
The final scene has a flock of pigeons who miraculously survived the nuclear war. However, since pigeons can fly, they could have come a considerable distance into the city from somewhere that was less affected by the radiation.
When Ralph is digging himself out of the tunnel, he often knocks himself against rocks. In the instances where he applies little force (such as knocking them incidentally with his elbow), the rocks move easily, showing that the rocks are not real. However, these rocks, which were lying upon each other, were irregularly shaped and so would be easily disrupted - even with casual touch of an elbow.
While Ralph is being pursued by Ben near the end, 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 building.
While Ralph walks around singing and playing the guitar, the whistle on the electric train is sounding without Ralph activating the whistle button on the transformer.
When the characters run through the street, the sound of their footsteps does not synchronize exactly with their footfalls; they are a bit off. It's a subtle effect but noticeable.
Not only does Ralph wait for five days before (easily) escaping, his ability to do so, including climbing the shaft ladder, is little impaired by his lack of food and clean water.
The recording Ralph listens to states the radioactive sodium half-life is just over two days and that it is deadly for about five days. If they were aware of this, many people would have taken refuge in bomb shelters, basements, caves, etc. and survived. Many families in the cold war era had plans for surviving nuclear fallout, and five days is not an excessive time.