Fake American: Angela Lansbury and Laurence Harvey, who are both British.
Plagiarism: It turns out Condon plagiarized several passages from Robert Graves' I, Claudius. This went unnoticed until a few years after Condon's death when a California software engineer started noticing the similarities, and even then it wasn't until a few years later still when the findings were widely published.
The scene where Marco tries to break Raymond's brainwashing using a deck of cards comprised totally of Queens of Diamonds is out of focus. Frank Sinatra didn't quite match the intensity of his first performance in subsequent takes, so they used the blurry one. It kind of works to represent Raymond's disorientation.
The fight scene where Ben punches his hand through a table is actually Frank Sinatra accidentally punching his hand through a freakin' table and breaking a finger. The injury didn't heal properly and bothered him for the rest of his life.
John Frankenheimer notes on the commentary that the scene where Senator Iselin argues with the Secretary of Defense was entirely ad-libbed.
Underage Casting: In an example where a Playing Gertrude causes this, Angela Lansbury was only three years older than the actor playing her son in the original film.