The rocket Von Braun picks up during his presentation looks very much like a Redstone and not a Saturn V.
In the episode "Operation Paperclip", when Von Braun is narrating the promotional film, he picks up a model of the Saturn V rocket that was used to launch the Apollo missions to the moon. But the episode takes place in the 1950's, while the design of the Saturn V didn't begin until 1962.
Mimi says her husbands works for a "local university." No one in Columbus would refer to Ohio State as such.