When the guy in the gray Neon yells at Macgruber (when he first sees the car), the car is an SRT-4 neon, and when he sets the car on fire, it is an SXT neon.
When Jeff throws MacGruber out of Cunth's gambling room and then breaks Macgruber's Blaupunkt, it is undamaged when Jeff bangs it against the window frame. But when he throws it next to MacGruber it is prominently damaged, with the housing bent way out of shape.
When MacGruber leaves the cemetery and sees the gray Neon in the parking lot, he starts breaking the windows while talking on the cellphone. He breaks both driver's side windows, then the rear window. The shot cuts to the Colonel with whom he is speaking. When the shot returns to MacGruber, he again breaks both driver's side windows - the rear window is still intact.
When MacGruber is shown in his dress uniform, he has no Medal of Honor or several of the other medals he was supposed to have won as described earlier in the movie.
During the opening credits, MacGruber is shown on a number of different passports. The one for Israel states his nationality as "Israeli." This is incorrect. It should say "Israel." By comparison, look at the one for Japan, where nationality is (correctly) printed as "Japan."
The newspaper mentions September 19, 2010, as a Saturday. It was a Sunday.
The newspaper (which is dated September 19th) mentions the president's State of the Union Speech. That happens around the end of January.
Each time MacGruber is handling a grenade it has a blue painted top. This blue indicates that the grenades are dummies and can not explode.
MacGruber is supposed to be a Navy SEAL, yet during the warehouse shootout he states that guns "scare him" and he doesn't know how to use them.