The Funeral - S1-E3
Deliberate mistake: Though it serves the drama and black comedy of the scene, it's highly unlikely a modern, let alone future broadcasting network would neglect the importance of delay (usually around 30 seconds) between recording and "live" broadcast. Specifically, to prevent unexpected gruesome incidents like the exploding head seen in this episode from making it to air.
Continuity mistake: In Episode 1, Nora tells Nathan that he isn't supposed to know if she is a human or AI, but later on in the season when the egg hunt is announced, it is clear that the prize is virtual funds for the Uploads, and actual cash for the Angels.
Continuity mistake: The countdown timer shows 59:18 left, but in the next shot the timer goes back up to 59:26. (00:09:14)