In general, I like it very much, but speaking as a former government employee there are some things that gnaw at me. The hiring practices, for one thing. Take the episode "Animal Control," for example. (Spoilers ahead, by the way.) At the end of the episode, after the Animal Control department is absorbed into Parks and Rec, Chris and Leslie appoint April the Deputy Director for Animal Control. That's not the way it works! Especially with a new position. You need to write a position description, and advertise it, and hold interviews, and only then can you actually hire someone.
Now, that same episode says that department directors are political appointees, nominated by one council member and confirmed by the full council. Which is weird for a municipal government, but OK. But Chris and Leslie explicitly say to April that deputy directors are not subject to approval by the city council, so she should have gone through a normal hiring process. They're at least consistent about it, at least; Andy and Ann got their jobs at city hall in much the same way. But I don't have to like it!
Another thing: it strikes me as wildly implausible that Leslie could continue working part-time for Parks and Rec even after being elected to the council. For that matter, it's unlikely that she could've even run for city council in the first place without having to resign from her government job. The Hatch Art prohibits government employees from running for public office if their position is supported in any way by Federal funds. Of course, the Hatch Act wouldn't apply if her position is funded entirely by municipal funds, but given how cash-strapped Pawnee has been in the recent past, how likely is that?
ETA: because I just saw it on Facebook and it's related to the topic at hand: