Slip-up Number 1: As you know, in the first movie , Austin Powers had his teeth fixed towards the end of the movie (1997). In the second movie when he goes back to 1969, his teeth are messed up again, since he wouldn't have gotten them fixed for another 28 years. At the end of the movie, when he goes back to 1999 again, his teeth are still messed up, even though he had them fixed two years before (in 1997).

Slip-up Number 2: When Austin Powers is in his Volkswagon Beetle time machine, the destination pad,(where the year is punched in), already says 1969, very dimly, before it's punched in.