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.
Continuity mistake: Whilst Neuman is having lunch with Hughie, when she asks "How'd surveillance go with Termite last night", she has her fork placed in the salad bowl. When the shot cuts to focus on Hughie, the fork is now in her mouth and then she lowers it back into the salad bowl. (00:17:48)
Glorious Five Year Plan - S3-E4
Factual error: The Boys use a Dodge Sprinter to drive around Russia. In Europe and Russia this Sprinter was only sold through Mercedes-Benz.
Proper Preparation and Planning - S2-E2
Continuity mistake: Frenchie has some decorations on his shoulders, shot changes and when back on Frenchie the decorations aren't there. (00:37:41)
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: In Russia, Soldier Boy is shown heading to the airport, He wanted to get to the US and start his revenge against his team. Problem is: he has no documentation and money to take a flight. Even if he stole the money somewhere, still would be impossible to travel without the proper documents.
You Found Me - S1-E8
Continuity mistake: When Mallory is holding the binoculars up to her eyes, next shot they're instantly down. (00:14:10)
Plot hole: Starlight, Kimiko, and Hughie are torturing Tek Knight by transferring millions of dollars to organizations he hates. Even though it's needed to move the plot forward, there is no way they could have known the routing and account numbers for those organizations.
Suggested correction: Both Starlight and Hughie are probably familiar with a lot of organizations that accept donations and gifts through their former jobs as political representatives. Why wouldn't they know the numbers?
Respectfully, that's a big leap. They were political representatives, not members of a trust or charitable foundation. Why would they have memorized the bank account numbers of random organizations? Not to mention the fact that at no time do Starlight or Hughie provide the account numbers to Kimiko. She just starts typing and bam, the money is transferred.