Continuity mistake: Elisabeth Shue is talking to Homelander by her car. As she gets her baby out of the car, she says "can we please just talk later" and has a muslin hanging over her right shoulder, turns around, and from the reverse angle the muslin is bundled up in front of her, not over her shoulder at all. Then the angle changes again and it's back where it was before.
Jon Sandys

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)
Plot hole: The nanny cam footage A-Train watches makes no sense. There's footage of him having sex with Popclaw, then static, then her accidentally killing the landlord. That would only happen if someone edited it together - there's no lead-in to her landlord situation, it just cuts right to his death and the Boys arriving. But they were in the bedroom well before that - either it's motion sensitive and should have caught the whole thing, or it's recording continuously and still should have caught the whole thing. Instead this digital recording acts like a VHS tape someone accidentally recorded over.
Jon Sandys
Suggested correction: Actually A-Train is holding the remote and it changes after he is pressing it against his forehead. He even looks at the remote after it changes, implying he accidentally pressed a button. The static shouldn't be there though as it's a digital recording.
lionhead