Continuity mistake: Dennis walks up to the computer to see the guy claiming to be their father carrying nothing, he puts his empty left hand on the bar, but when the shot switches he is holding a coffee in that hand. In the shot right before the opening credits the coffee is gone again.
Continuity mistake: When Dee tells the gang someone is contacting her claiming to be their dad, only one coffee cup is next to Dee, on the side closest to Mac. She lifts that cup and puts it towards her lap, but when the camera shows the computer, the cup is back and another cup is on the other side of the computer. When the camera zooms out both cups are gone again.
Continuity mistake: When Mac is eating the peanuts there are no crumbs next to the bowl and his beer. When he lifts up his beer to tell Dennis that it's irrelevant there are crumbs. When the shot zooms out to Dee on the computer, the bar is clean again.