Factual error: Looking at a nuclear explosion that close will burn your retinas irreparably. One can be blind 30 miles away, just by seeing the flash. The little girl at the start is looking directly at the explosion when it hits, and continues to watch.
Continuity mistake: This show has been widely declared as canonical with the games, by the makers of both this show and the games. The game Fallout 4 establishes the date and time that the bombs drop: Saturday, October 23, 2077, 9:47 AM East Coast Time. Which means it was 6:47 AM West Coast Time. That's a pretty weird time of day to schedule a kids' party with lots of guests and a hired celebrity cowboy.
Suggested correction: They changed a lot of subtle things from canon for the show. Also, all games have got some inconsistencies between them as well. In the show, on the TV, there is a clock that says it's around 9:30 AM the first time we see it and 10:45 when they cut the cake, so it's close to the afternoon and not very early in the morning. The position of the sun confirms this.
So, if it's 10:45 West Coast time, that makes it 1:45 PM East Coast time. Would you carry on a birthday party if the other side of the country got nuked four hours ago?
The show is not taking place on the East Coast; it's on the West Coast in California. The show made it so it was 10:45 AM on the West Coast when the attack began. The attack happened all over the US simultaneously. This is not a mistake but done intentionally. You can call it a deliberate mistake. Definitely nothing wrong in the continuity of the show.
