Other mistake: The article on the right-hand side of "The Olympian" seen at the end of the film is the same one seen on the right hand side of the "Daily Journal of Commerce" that Tracy looks at after chopping down the tree. Although the 2nd column of print in the "Daily Journal of Commerce" is now the 1st column of print in "The Olympian."
Other mistake: When we see the front page picture of Mike with the alcohol and joint, he's pouring the alcohol over his bottom lip and chin, going down the front of his shirt. This doesn't match what we see him do. It does appear that Mike spilt alcohol on himself when off camera, but the wet spot is on the right side of his jacket, but not down the front.
Answer: A major police department would probably not allow modifications to an official vehicle, even if it was assigned permanently to a particular officer, due to safety or insurance concerns. That said, many departments do use high performance or exotic vehicles seized during crimes under various forfeiture laws. Most times these are for promotional purposes, but I do know of a Florida department that used a souped-up Dodge Hemi-Charger painted in standard department livery for traffic enforcement.