The Bemidji police car fleet exclusively comprises vehicles built in the 1990s - some of which date back to 1992. Given the high mileage, intensive use and harsh Minnesota weather, it's highly unlikely that any of these vehicles would remain in service in 2006, let alone an entire fleet.
When Mrs. Nygaard lifts her soup spoon, it's in her left hand; when she lowers it, it's moved to the right.
In episode 8 when Lester recognizes Lorne in the club in the story he is telling he says: "...And it hurt but I didn't want to look stupid so I try it again..." but when the full conversation is shown in episode 9 he replaces the word "stupid" with "dumb".
In season 2, none of the phone booths have service lines to them, and while the one at the gas station could, however unlikely, have an underground feed, the one in the country would certainly not.
At the beginning of each episode it is stated that the events took place in 2006, yet the last 2.5 episodes actually take place in 2007.