A picture of Madam Secretary on Leslie's wall. Similarly, when Leslie meets Joe Biden in the fifth season, she thinks he's going to ask her to replace "Madam Secretary".
Tom's angry insistence on a high thread-count in his bedsheets is a reference to Aziz Ansari's stand-up bit about buying Luxury Linens brand sheets, only to find out the package lied about the thread count.
Tom tells Ann that he couldn't afford to get toppings on two pizzas, because he's not Zuckerberg.
Nick Offerman is a real life carpenter, and his character Ron makes several references to projects he's actually performed.
One episode has Donna live-tweeting a movie, which is based on Retta's real life live-tweets of shows.
Banned in China: Sony didn't dare to broadcast the infamous episode "Sister City" (which dealt with a very point-on parody of Venezuelan military government officers) on its Venezuelan feed, and it's very improbable that the series even airs on open networks.
The Danza: Ann's friend Justin Anderson is played by Justin Theroux.
"In Operation: Ann," one of Ann's potential suitors is a Phish fanatic named Harris, played by show writer Harris Wittels.
Real-Life Relative: Will Arnett has a cameo as a creepy guy Leslie dates in one episode. He was formerly married to Amy Poehler (Leslie) in real life. Also, Nick Offerman (Ron) and Megan Mullally (Tammy 2) are married in real life.
Screwed by the Network: The show was brushed aside for mid-season replacement Outsourced, which was hated by critics and did not make it past a first season. The show's fifth season narrowly avoided being cut to 13 episodes as a precursor to cancelation, but the season was officially granted a full 22 episodes.
Averted with it's renewal for Season 6, although the failures of every other comedy on the network and the ending of The Office forced the hand of NBC. The only other comedy to survive was Community.
There's also a throwaway line in the season premiere about Andy giving up beer in order to explain Pratt's fitter physique.
Throw It In: The show makes use of varying degrees of improvisation. The most frequent example are the "addressing the camera" scenes with many jump cuts between jokes; these are usually the result of letting the actors run off-script (especially with Amy Poehler).
The show's co-creator also said at a panel discussion that his favorite joke in the entire series - Andy's line "Leslie, I typed your symptoms into the thing up here and it says that you might have...Network Connectivity Problems" - was made up on-the-spot by Chris Pratt.
Word of God: Ron's nickname for Marlene Griggs-Knope was not specified in the script, and the nickname is heard in the episode as "the Iron-[bleeped] of Pawnee". According to Aziz Ansari's twitter page, Nick Offerman improvised "the Iron Cock-Shredder of Pawnee" at the table reading.
What Could Have Been: Deleted scenes and DVD audio commentary reveal that several Pawnee townspeople would become more heavily recurring characters in future episodes. These characters included conspiracy-theorist Barry, anti-parks advocate Kate Spivack, and Andy's neighbor Lawrence. When the Pit 48 plotlines were demphasized in the next season, the need for these characters diminished. However, Lawrence made several cameo appearances in later episodes. Barry appears very briefly in season two in the episode "Sister City", though he only has lines in a Deleted Scene.
Even after the original plan for P+R being a spinoff of The Office was scrapped, there was one idea of creating a connection for the two, where the Dunder-Mifflin copier would break, be fixed and refurbished, and then shipped to the Pawnee Parks and Rec department. Never happened.