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)
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)
Continuity mistake: They eat at JJ's Diner and the waffles are square. Throughout the remainder of the show, at JJ's Diner, the waffles are round. Unlikely they'd switch their waffle iron from square to round. Also, the old retired waffle iron Ben and Ann get Lesley is round. (00:03:20 - 00:16:10)
Visible crew/equipment: When Dianne's daughters have locked themselves alone in the room, just as Jerry is about to put the keys in the door to unlock it so they can prevent the girls from cutting their hair, the boom microphone dips into view in the room where the girls are alone. This boom mic is not from the "documentary" crew. (00:13:25)
Character mistake: During Garth's Filibuster, the Marvel characters come into the Star Wars universe because Thanos is using the Infinity Gauntlet's Reality Gem to cross realities. The gem allows the wielder of the Gauntlet to MOLD reality to his desire, but an Infinity Gauntlet does not work outside it's home universe/dimension, so Thanos wouldn't be able to "jump from different realities" with it. Someone that well-versed in the Marvel Comics universe would know this.
Continuity mistake: Andy is explaining that he wanted his coworkers to steal something from him so he can practice his investigating skills. In one shot his sunglasses are hanging at the middle of his torso and when it cuts to a closeup and back out the sunglasses have magically traveled up to his neck as he exclaims "did you guys steal my sunglasses too?" (00:15:00)
Continuity mistake: When Ingrid and her team show up late to the meeting at City Hall, as Ingrid takes a seat we see under the table that the actress is wearing dark sneakers, but Ingrid is wearing off-white heels when she enters and exits. (00:08:25 - 00:11:25)
Continuity mistake: In the previous episode, Tom meets Dr Nadia who agrees to date him, and Andy returns from London saying he will be in Pawnee for "19 hours." In this episode, Tom claims Nadia has been hanging out with him for a week, and Andy is still in Pawnee, even though she should have returned to London days ago.
Continuity mistake: When Ben and Leslie approach the commissioner about the recount, there are two guys sitting down behind Jen. The camera follows the commissioner leaving the room and then momentarily shows Leslie and Ben. As Jen is lying out on the table the two guys have now disappeared. (00:13:00)