These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Tom's South Asian background is the subject of much japery, and even Leslie can't seem to get it through her head that he's a US-born citizen. This would now seem to be Early Installment Weirdness as Leslie developed into a character who wouldn't make insensitive "Michael Scott"-type remarks about race.
Christian fundamentalists, as represented by the character of Marcia Langman.
Base Breaker: April Ludgate. Some fans love her for her Snark Knight personality and being a Jerk with a Heart of Gold capable of true acts of kindness. Others hate her and think she's just a Jerk Ass that gets away with being lazy and mean with no repercussions. They also hate Aubrey Plaza's monotone delivery.
Critical Research Failure: Andy asking for Power Rangers to be brought back - at the time, the show was brought back from cancellation and was airing on Nickelodeon. In fact, it'd only been off the air for one year before that, and even that was 3 or 4 years earlier. Then again, this does fit nicely with Andy's characterization.
When Ron brings a pig to slaughter for meat. To a public annual BBQ with children and families attending. It becomes funny when he starts asking kids to join in on the slaughter, and even more when he gives the sheriff his "authorized documents" (a piece of paper with only the words "I can do what I want. Ron.")
Crowning Music of Awesome: Has there ever been a television moment more triumphant than the Harvest Festival montage set to Tom Petty's "American Girl?"
Rises to Memetic Mutation given its acknowledgement by the cast; during one panel between the cast, Greg Daniels was talking about a moment between April and Andy in "Rock Show", which he mentioned was in season 1, then gave a knowing pause at what he just said, causing everyone in the audience to laugh and Aziz Ansari to yell, "Don't bring up those shitty episodes, man!"
Growing the Beard: The series is generally regarded as having come into its own in season two, when the show stopped trying to just be a The Office clone and started finding its own voice. This is remarkably similar to The Office itself, where it too grew the beard in season 2 by establishing a distinct identity and brand of humor away from its inspiration and found an audience. Fitting enough when the show aired in Germany the entire first season was cut out. By the end of the season, it's pretty much outgrown its Early Installment Weirdness and come into its own identity.
It grew it further in Season 3 with the introductions of Ben and Chris, adding some more variety and chemistry to the cast after getting rid of bland and unintresting Mark at the end of last season.
Hilarious in Hindsight: One episode notes Ann's taste for terrible Lifetime movies, and has her describe a stereotypical parody of one. This becomes funnier given that co-star Rob Lowe was cast in a Lifetime movie as Drew Peterson.
Thanks to the US federal government shutdown in 2013, the Pawnee shutdown between Season 2 and 3 becomes a lot more realistic.
Andy's asking the goverment to bring back the Power Rangers is now making rounds with the announcement of a third movie for the franchise. Thank You, Star-Lord!
Andy, during his wedding, says that he's the luckiest man "in the galaxy". It's a funny choice of words considering Chris Pratt would go on to star in Guardians of the Galaxy.
Ho Yay: Lampshaded in one episode when Ron makes a rather... suggestive moan when Andy polishes his shoes.
Jerkass Woobie: As much of a narcissistic, lecherous Jerkass as Tom has been, one can't help but sympathize with him as he discovers that he truly loved his ex-wife Wendy.
Magnificent Bastard: Greg Pikitis, who manages to not successfully vandalize the park statue every year, makes Leslie look like a lunatic, sneaks into the office and trashes the place using a disguise, breaks Andy into tears without even saying anything, and always gets himself out of trouble by hiring an woman off Craigslist to pretend to be his mom. Andy even relents that the kid is pretty impressive.
To a lesser extent, Chris. He goes from a rather flat, Innocently Insensitive fitness nut to a well rounded fitness nut with a load of personal problems.
The Scrappy: Mark. While other characters always had some semblance of originality to them, he was an incredibly bland Jim clone from the start. Thankfully he also became one to the writers, who removed him from the show entirely when it began developing its own style.
Strangled by the Red String: Leslie and Ben just sort of... get together. They become a very cute couple, but it's quite odd as the transition from coworkers to lovers is awkward at best.
Strawman Has a Point: In the "soda tax" episode, if the Paunch Burger executives weren't so outlandishly double-speaking they'd probably come off sympathetic. They quite reasonably point out that they're merely selling what the Pawnee market wants to buy, even if it's unhealthy. Seasons earlier, Ron agrees that being allowed to stuff your face with unhealthy crap and die in your 40s if you really want to do so is a facet of American freedom.
In "Bus Tour", Bobby Newport's father dies. When Leslie tries to comfort him, she tells him that her mother was a great athlete and to get her love, she joined track. She hated it and came in last in the final race. Leslie thought she failed, but her mother was proud anyway. Bobby uses this story as an anecdote about his dad, even changing the ending to claim he won the last race. Leslie thinks its just ripping off her story but, Bobby used it because her story was better than anything his father has ever done for him.
"Recall Vote". Leslie loses the recall election and is distraught for almost the entire episode.
The ending to "Ann and Chris" when Ann and Chris say their goodbyes.
Unpopular Popular Character: The only person who can stand Jean-Ralphio in-universe is Tom (and even he has admitted he could use better friends). Out-of-universe, he's one of the most celebrated recurring characters on the strength of Ben Schwartz's gloriously obnoxious performance.
You can't help but feel sorry for Ben in "The Harvest Festival" when people won't leave him alone about Icetown and then he leaves and tells Leslie that he's probably the source of the Curse and it's all his fault that Lil' Sebastian ran away and the power went out.
Leslie in Season 6, who seems to be getting hit with Finagle's Law on anything she tries to do for the town in addition to being recalled from city council.
Chris in late season 4 and early season 5. He looses his girlfriend, and rapidly finds his life empty and miserable, tries for Ann again and gets rejected, all of this cumilating in his body breaking down in the second episode of season 5 after he realizes he has 'nothing and no one"
Andy becomes this in season 2 and becomes a bigger woobie as the show goes on. He spends most of season 2 living in a pit and desperately trying to fix things with his ex-girlfriend (which he fails to do) and in general he's such a socially-awkwardmess that it's near-impossible to not pity him.
Bobby Newport. Yeah he's competing against Leslie, but only because he's desperate to earn his father's approval. And when his dad dies he's utterly devastated.