Ivana Humpalot: Do you know how we keep warm in Russia?
Austin Powers: Oh ho ho! I can guess, baby.
Ivana Humpalot: We play chess.
Austin Powers: I guessed wrong.
During the bedroom scene with Felicity and Fat Bastard you can clearly see the air hose that fills his suit when he rolls over in the bed.
In the opening musical sequence (in the pool) Austin and the water ladies jump out of the water, the lady behind Austin to his left, can clearly be seen laughing because her water cap has fallen down.