Visible crew/equipment: When Dewey yells for Lois because the bow was put on the present, if you look to the left of Lois, you will see a crewmember kneeling down, handing Lois the Red Dress, who is holding a bucket of water. He quickly gets out of the camera's view. [This is on the DVD of the first season. Someone said on the audio commentary that after catching it, they deliberately left it in to see if anyone would spot it. It's still a mistake, but that's why it's there.]
Other mistake: Cook and Effy manage to fall through Pandora's Mum's wardrobe, into the next door neighbor's bedroom. But this is not possible as the neighbors' houses are detached.
Episode #1.3 - S1-E3
Continuity mistake: Vera fires the gun several times, and later tells Justice Wargrave that the gun is empty, meaning that all the cartridges in it would be spent. When the judge loads his one bullet into the chamber, he does so in a gun where all five cartridge svisible are unspent.
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.
Kobol's Last Gleaming (2) - S1-E15
Visible crew/equipment: In the scene where Starbuck attempts to retrieve Apollo's arrow, a crewman in a red tee shirt and dark vest can be seen standing just behind and to the right of the display case as she is shooting out the glass.
Free for All - S1-E4
Continuity mistake: Throughout the episode, Number 6's lapels switch from having solid to broken white piping and back again.
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)
Plot hole: Hippolyta tells Hawkgirl of Aresia's background of being born in the outside world, the war in her country and right up to her drifting to the shores of Themyscira. It would be impossible for her to know anything of Aresia's background as in part two, it's explained that the captain of the ship who saved Aresia died shortly after reaching Themyscira and therefore would not have been able to tell Hippolyta anything.
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.
Girl Trouble / School Dance - S3-E18
Continuity mistake: Besides the fact that when Helga is sharpening her pencil, the desk arrangement changes, one of the students visible when she looks at Arnold is... Helga. This happens because the shot is taken from the episode "Helga's Love Potion."
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)
The People vs. the Fonz - S11-E11
Factual error: When the Cunninghams are talking about Fonz's trial, Mr. Cunningham can be seen wearing a digital watch. Digital watches didn't exist in the 50's.
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.
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)
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.
The Séance - S1-E7
Continuity mistake: After Lucy tells Mr. Merriweather that he's invited to the seance, when it cuts to Lucy unfolding the card table legs, note the couch behind her with one normal seat cushion on the left, but in the next wideshot there's an additional shorter cushion under the normal cushion. The small towel also repositions itself neatly on the couch. (00:11:55)
Revealing mistake: Any time any character is driving a Suburban, or any other vehicle with a column mounted shift lever, the shifter is in park while they appear to be driving.
House Party - S2-E5
Continuity mistake: Kelly said her youngest brother can burp his whole name Kenneth Leonard Kapowski in one burp. However in the previous year, Kelly had an infant brother named Billy. According to this info, unlikely Kenneth would be younger than Billy.
Suggested correction: Kelly can have more than one brother because in the episode where Kelly gets her job at the Max she said "I cook every night for my 11 siblings". So he could be younger or just have a nickname.
The mistake is valid because she says her "youngest" brother, not "younger." In the episode "The Babysitters" (which was meant to air in season 1 and produced before "House Party"), her brother Billy is an infant and says his first words. Kelly has 6 siblings and she never said she cooked for 11 siblings when getting a job at The Max. She says she sets the dinner table for 9 people three times a night.
Ironically, the show only reveals 5 siblings each in their own individual episode. (#6 is unknown). Bennett (mentioned), Nicki (seen), Kyle (voice heard only), Kenneth (mentioned), Billy (seen) are the 5 of 6 siblings revealed.
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.
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).