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)
Episode #1.1 - S1-E1
Other mistake: When Tony walks by the school there's a girl in a blue dress with a hula hoop that can't stop staring at the camera.
Episode #1.5 - S1-E5
Continuity mistake: The candle next to the mattress Julian Kane is passed out on is lit and burning in the previous episode. This one opens with the child finding Julian, but the candle which was burning in the previous scene is brand-new and unlit, despite supposedly having been burning all night. (00:26:00)