Revealing mistake: When April is searching for Donna Meagle on "iGoogle" you can see that it is a HTML document that they've most likely made themselves. The URL says "C:\User\pnr\Desktop\igoogle\igoogle search\donna.HTML". You can also see that the internet browser says "Google Search" but they've used "iGoogle" everywhere else. (00:04:30)
Continuity mistake: When volunteering with Kaboom, Leslie says they are building in Eagleton, which she describes as "two towns over." As the show continues we visit the Eagleton/Pawnee border and the neighboring towns become a plot point for many episodes. (00:01:35)
Factual error: Leslie mentions that Eagleton is "2 towns over." We in later episodes see the border wall between them (S3E12), indicating they're right next to each other.
The Set Up - S2-E13
Continuity mistake: As they are celebrating April becoming an assistant, her drink is dark red (probably wine) and in the next shot suddenly becomes a bubbly yellow (probably champagne), and in the next shot turns back into a red liquid. (00:20:55)
94 Meetings - S2-E21
Plot hole: April tells Ron that she's always known that he's Duke Silver because her mom has all his albums. So why didn't her mom freak out when Duke Silver appeared on her doorstep or, if she somehow didn't realize that Ron is Duke, even mention the resemblance? (00:20:35)