When Howard storms into the apartment Sheldon gets scared because, as he says later, Howard looked taller. This is because of his heeled shoes which, Sheldon says, "fool no one" in The Dead Hooker Juxtaposition (2009). So Sheldon shouldn't have been fooled.
The claim that California is a property state does not cover property acquired before the marriage. The letter was clearly Howard's property from before marriage.
Sheldon says that the Copyright law allows him to quote some snippets, but that's wrong - he can't do it for an unpublished work, which is the most probable state for Bernadette's diary.
Although the gang claims all of their examples are possible it's not true. Everyone refers to it as a letter however Raj and Bernadette's aren't letters.
It makes no sense for Howard and Bernadette not to have a ladder handy, precisely because both are so short.