Continuity mistake: When Agatha is talking to Herbert at the police line, the position of her arms varies over several shots.
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 Eastern 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.