Factual error: When we have the last montage of jokes about the shape of Dr. Evil's rocket, it is 1969. You can tell from the clothes and the fact that Dr. Evil left in the rocket from the moon base and Austin and Felicity had to go forward in time from the moon base to get back. Now in this montage we see Woody Harrelson (in a cameo) who is apparently an accomplished actor in 1969. One small problem: Harrelson was born on July 23, 1961 and therefore would be around 8 years old.
Factual error: When Austin is photographing his frozen self, you can hear a motordrive on the camera whirring away. However, the camera doesn't have a motordrive attached, and anyway is a Nikon F with Photomic head which doesn't have a socket for a motordrive.