Other mistake: When Cat picks up the can of Leopard lager which is invisible to Lister, he shakes it, pops the cap and sprays Lister with foam. The foam is visible but the can remains invisible, and that makes no sense. If we are seeing the scene from Cat's point of view the can and foam should both be visible, and if it is from Lister's then neither should be.
Other mistake: When Phoebe and Ross are at JFK, some of the people who are at that airport are the same people who are also at Newark. It's particularly funny to see the people behind Ross and Phoebe at JFK when Phoebe claims they're on their honeymoon, and when it cuts to Rachel at Newark as she's looking for her boarding pass, those same people are there too.
Other mistake: In an earlier episode where Edie and Susan are driving Martha Huber's ashes to the lake to be spread, Edie gets a flat tire and Susan changes it. In this episode, all the girls are driving with Edie's ashes and they get a flat tire. Susan asks "Does anyone know how to change a flat tire?" Did she forget how?
Other mistake: Private Duke Slater's utility uniform shirt is different from the other Marines. Duke's uniform has square pocket flaps with the button exposed, an exposed button front shirt and the sleeves do not have button cuffs. The other Marines' uniforms have tapered pocket flaps with a hidden button, a hidden button front shirt and the sleeves have button cuffs. (00:05:00 - 00:06:00)
Other mistake: Crowley shows acute discomfort while inside the church with Aziraphale and the Nazi spies as he is on consecrated ground. However, (spoiler alert) once the bomb destroys the church he is perfectly comfortable. The key word here is "ground" - it is the land upon which the church stands that is consecrated, not the building itself. (This allows churches to be rebuilt if they are demolished or destroyed.) Crowley should still be in considerable discomfort after the church has been blown up.
Other mistake: As Young Sheldon is a prequel series to Big Bang Theory, this episode is at odds with episode 2-13 of Big Bang Theory, "The Friendship Algorithm," in which Sheldon is unfamiliar with books like "How to Make Friends and Influence People," which he reads in this episode of Young Sheldon, produced nine years later but taking place twenty years earlier.
Other mistake: The opening credits for season 5 show June coming out of the front door with a pitcher of what looks like iced tea, and calling for Ward, Wally and Beaver who are all working outside. But the door opens by itself as she comes out, and then closes by itself behind her. If the entire family is outside, who opened and closed the door?
Other mistake: Episodes 4 and 5 of season 1 aired noticeably out of order. In episode 4, "The Nanny," Alex's former Nanny, Rosalba, comes to work at his podcast company, and its name, "Ajana," is mentioned a few times. But episode 5, "The Mother-in-Law," starts with the company unnamed; over the course of the episode, Alex learns of the concept of "ajana," the unknown, from his mother-in-law and chooses it as his company's name.