Old Friends, New Names - S1-E1
Continuity mistake: Pete tells Tiff that he has so many questions. She reaches his face and holds it between her hands. She has two fingers on his ear, then her index only, then the fingertips are on his chin. (00:02:10)
Visible crew/equipment: You can see the camera in the backseat as they pull into the gas station.
Episode #1.1 - S1-E1
Continuity mistake: As Ricky Gervais walks by the school where his nephew is, a "chubby little ginger" shouts "pedo" at him. He stops and holds one of the bars of the railing, third from the pillar. In the close-up, you can count more bars than that, showing he is in a different position altogether. (00:07:00)
Continuity mistake: Kate arrives in front of the newspaper. Directly behind her a guy a bit on the chubby side is arriving as well. But he already was in the crowd shown before, looking at the dummy. (00:11:40)
Continuity mistake: Ashley Barrett is first seen behind Homelander, but then in the next shot she immediately jumps in front of him. (00:19:32)