In the first scene John and Helen are having a conversation in a room. Suddenly a nuclear detonation is seen through the window. An uproar is heard at the same time of the initial flash, then we hear a big thunder. Even if we consider the first noise as being not the direct noise from the explosion but some secondary effect of the radiation wave (which travels at the speed of light), the main thunder comes 6 seconds after the flash, therefore the detonation must be about 2 Km (1.24 miles) away: they would have been killed almost instantly. Given the apparent distance of the mushroom, the thunder would have been delayed by 60 seconds.
Muscular Dystrophy is a sex-linked trait with its gene located on the X chromosome. Thomas would have inherited a Y chromosome from his dad, John Smith and his X chromosome from his mother. She gave him the faulty gene.
When Thomas Smith takes a book from a shelf, a copy of "Mein Kampf" becomes visible with Adolf Hitler's first name misspelled as "Adolph".
The heat flash of the nuclear detonation would have ignited the curtains and the surrounding trees.
The shock wave of the nuclear detonation is shown reaching the Smiths about 4 seconds after the flash and barely rattles the house. The blast should have taken about 30-40 seconds to cover that distance and would have shattered the windows.
The time is set in 1962. When Hawthorne Abendsen plays with some coins during his monologue, one is a 5-Deutschmark coin with a design that was issued only in 1975.
Near the end of the episode, Abendsen takes coins out of his pocket and puts them on a table. Among them is a U.S. Franklin Half Dollar, minted from 1948 to 1963. However, since in the alternate historical timeline, Washington, DC was destroyed in December 1945 and the war ended in 1947, these coins would not have been minted.
The projection technology seen in the Nazi war room is inconsistent with other technologies seen in the series and inconsistent with real-world technology timelines.