Factual error: When Austin sees the reflection of the assassin in Robin's eyes, it should be a reverse image since it's a reflection, but it's not. The assassin is seen raising his right hand both times when the reflection should make it look like it's his left.
Factual error: Through most of the film, a lot of the cars used are left hand drive, while in the UK cars are right hand drive. While left hand drive cars are occasionally seen in the UK, they're very few and far between.
Factual error: The song American Woman by The Guess Who is being played at the party when Austin goes back to 1969. Cool song, but it wasn't released until 1970.
Factual error: During the first joke about the shape of Dr. Evil's rocket, we see Willie Nelson. But he looks the same as he does today, when he should be thirty years younger.
Factual error: The rocket launches from Dr. Evil's base literally inside the main room with all his cronies in it. As it rises, the blast from the engines would have incinerated everyone left behind.
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.
Answer: It's called "Soul Bossa Nova", by Quincy Jones.
Grumpy Scot