Continuity mistake: J. Edgar takes his secretary-to-be on a date and tries to impress her by showing off his card system for cataloguing books in the Library of Congress. When he runs to the book shelves he brushes past an open book set up on a display stand - sitting on a sheet of glass. The glass moves when he touches it and hangs off the edge of the table. When he returns seconds later the glass is back in place, centered on the table. His date did not move; she was still standing where he left her a few feet away and they were the only two people in the Library.
Continuity mistake: In the scene where Margaret Thatcher is teaching her daughter Carol to drive, you see Margaret's window partially open but just as they near-hit the cyclist, her window is down just enough for her to stick her hand out but in the next shot its back to being partially open.