When Valeri learns the truth about who Reggie is, she asks Michael: "He wasn't knighted by Prince Harry in a ceremony televised on CNN?" and Michael says "I think Harry is only 6." Prince Harry was actually 10 at the time the movie came out; he was born September 15, 1984, and the movie came out on March 19, 1995.
When they switch camera angles while Jay Mohr eats a turkey sandwich, it's obvious that although he didn't bite into the sandwich it looks smaller than it did before.
When Jason Alexander walks to the door to leave the roof in the scenes where he realizes that he is falling for Valeri, the green door is closed, but cut to the next scene and suddenly he's walking through a totally different door.