Shakespeare wears an obvious bald cap.
The full-surface spot reflection on the editor's glasses reveal they are flat, just for looks. (at around 6 minutes)
Julius Moomer incorrectly says to William Shakespeare that he had been dead for 1000 years when in actually he had only been dead for 347 years in 1963.
The bus driver spends far more time watching Julius than would be considered safe. Also if a bus driver throws everyone off for acting weird he would have very few passengers, which may explain why there are so few other passengers seen.
The woman in the bookstore asks how anyone in their right mind could get rid of Gil Hodges, indicating this would be after Gil was traded to the Senators in May, but he was just mentioned as a player at bat for the Mets.
Mr. Hugo calls Shakespeare "the kook in knee breeches." Shakespeare was wearing trunk hose rather than knee breeches.