Towards the end when Lemmy and Natasha get into their car while all the Alphaville residents are incapacitated, cars can be seen driving past, while the drivers should have been knocked out.
Towards the beginning, the term "light years" is used as if it were a measure of time, when actually it is a measure of distance.
When Lemmy shoots the man in his hotel room, smears on the mirrors from the blank cartridges' charges are plainly visible, instead of a bullet holes or broken glass.
When questioned, Lemmy Caution states that he drives a Ford Galaxy. It's actually a Ford Mustang.
Just before Lemmy Caution/Ivan Johnson meets Natasha Vonbraun, around 10 minutes into the movie, you can see the crew in the mirror when the camera pans.
After Lemmy has shot Professor Vonbraun, he runs down a staircase and throws open a glass door. As he does so, the reflection of the cameraman can be seen clearly in the door.