Visible crew/equipment: When Nina's just been shot, and makes it to the barn to call CTU (around 7.10am), while she's speaking on the phone there's a cameraman visible on the right hand side (DVD). (00:12:40)
Deliberate mistake: When the Doctor begins to "fade" in the transporter room his mobile emitter fades with him. Since it's made of solid matter and is not a hologram, this shouldn't be possible.
Rockets, Communists, and the Dewey Decimal System - S1-E2
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.
The Mysterious Affair at Styles - S3-E1
Plot hole: Can't fault this massive plot hole to the adaptation, but to the source material; the culprit (forgetting the stupidity of writing an incriminating letter detailing the plan to murder someone, and put it in a desk he shares with her) since there are people outside the room that are about to enter, tears the letter in 3 neat vertical strips, rolls them, puts them in the vase on the mantlepiece, and then opens the side door to slip away...instead of simply pocketing the letter and going through that same door. Nobody was going to search him or anything and could have burned it, torn it into confetti, anything, later. It takes way way longer to do what he did, which needed him to stay there in the room increasing the chances of being found out. And of course he and his accomplice do not retrieve the letter after.
Character mistake: When Beth and her mother discuss the agent's fee of 15%, Beth says it is $49.54. However the prize money was $500, the expenses were $172.30, which leaves them $327.70. 15% of $327.70 equals $49.16. (00:10:00)
Revealing mistake: Watch the opening sequence of this episode very carefully - Clarkson, May and Hammond are not in Downing Street (they are on a set that stands on the BBC backlot) and library footage of the Prime Minister is cleverly edited in to make it look as if they were there at the same time. Even taking into account the fact that the Prime Minister's security service would never allow such an intrusion onto Downing Street, the line up of the shots does not quite match - our three intrepid heroes should be visible in shot when the Prime Minister is shown exiting number 10, but they are nowhere to be seen. It is all sleight of hand and clever editing, but detectable if you watch carefully enough.
While You Were Sleeping - S1-E2
Other mistake: When Sherlock was slapped, he later says he was surprised because the girl who slapped him was a "lefty." Then he rubs his right cheek and says it's leathery from all the slaps he's gotten, while the left is soft. This is backwards - anyone hitting him with their right hand would hit his left cheek.
It May Look Like a Walnut! - S2-E20
Character mistake: Rob is having a nightmare, part of which involves the disappearance of his thumbs. When he finds Laura at home, the script calls for him to say, "I want you to help me get my thumbs back," but he actually says, "I want you to help me get my thumb backs." His thumbs are also still there but hidden (you can see a portion of them in one frame of the episode).
The Suitcase - S4-E7
Factual error: At the beginning of the episode, the male employees are all discussing James Bond. It is mentioned that 'James Bond goes underwater, he met a girl underwater'. This refers to the plot of the movie 'Thunderball' (it does not occur in the Thunderball novel, nor any novel or film prior to this). The main plot of this episode centres around the Sonny Liston VS Cassius Clay fight in May 1965, and 'Thunderball' was not released until December of that year.
Continuity mistake: After Buffy finds Morgan's brain, Willow pulls up Morgan's school file on one of the library computers without even touching the keyboard. One moment the monitor is on the desktop, the next it's showing Morgan's file.
Other mistake: When Lucy is in the cafe watching the mother and her children, the mother repeats the same dialogue.
The Uniform - S2-E11
Character mistake: While handcuffing an auxiliary officer in his apartment, there is a poster on the wall reading, "attention military personal..." Personal is misused. It should read "attention military personnel." (00:16:02)
Continuity mistake: When Megan is running late to pick up her daughter and friends from a sleepover, she arrives in the medical examiner car with Peter. The girls walk towards the car. Megan then gets out and introduces herself to the friends. The girls dump their bags on the ground and the two friends go to get in the car. Her daughter stands by the bags and asks 'who are you?!' to Peter. He explains who he is and that he works with her mum. - however in a previous episode her daughter goes to her work place and interviews all the staff, including Peter. (00:17:35)
Visible crew/equipment: When Kim is talking to Joan the security guard, a crew member drinking a cup of coffee can be seen in the dojo.
Confinement - S2-E5
Continuity mistake: Ruby asks Ash where the the Kandarian Dagger is. He says that it was confiscated by the police. In the previous episode, she had and used it, and they have not interacted in the intervening time period.
Other mistake: When Theo is thinking back to when Steve offers to share the royalties from his book, Shirley is heavily pregnant with her daughter. However, on the table next to Theo, is a photo of Shirley's son and daughter, as they are in the present.
Visible crew/equipment: In the first scene of the episode, a crew member is visible through an open door beside the staircase.
Continuity mistake: Ruth is seen in a flashback. The young Ruth has a mole on the left side of her face, as does the adult Ruth. But in one shot, when she is slapped by her father, the mole appears on the right side. (00:20:00)