Revealing mistake: In the scene where Austin and his allies burst through the big blue door, right before "Secret Agent Man" begins playing, the door explodes, and you can clearly see that it's made out of wood, even though it's painted to look like and is meant to be metal. This mistake is even mentioned in the director's commentary on the Austin Powers DVD.
Revealing mistake: During the Honeymoon scene when Austin and Vanessa are both naked, Austin sits down on the couch - I think it's the computer that covers him up. But if you look closely, you can see the G-string he's wearing. It's flesh coloured and hard to see, but it's there.
Revealing mistake: There are close-ups of Burt Bacharach playing piano and singing to Austin and Vanessa on top of a "bus" as they cruise through Las Vegas. From a long shot as the vehicle travels by, it's very obvious that it's not Burt playing, but a stand-in.
Revealing mistake: When Austin encounters the fem-bots, the main one begins to gas him. Then camera pans to her back, revealing the hoses emitting the gas.