After playing Gin Rummy, she says that'll be $225.10. When he counts the money out of his pocket, he only counts out 3 bills. No combination of 3 bills could possibly equal $225. He does take the 10 cents out after that.
While playing Gin Rummy, Harry deals Billy one card too many.
Stage man quickly hides behind curtain in apartment on the left side of the screen.
Set in Washington DC, obviously not filmed there. Airport scene filmed at Burbank Airport.
The art museum is supposedly in Washington DC, but we see Renoir's "Jean as a Huntsman" which is at the L.A. County Museum of Art (LACMA) (where the scene was filmed).
The entire movie takes place in the Willard Hotel. However, the view outside the windows of the set for Harry's office, supposedly inside the Willard, is of a large photo of the Washington skyline that actually has the Willard itself in the middle of the photo, looking to be about 4 blocks away.