Character mistake: Throughout season 3, whenever someone visits Henry in prison, the word "VISITOR" on their visitor tags is misspelled as "VISTOR."
The Magician - S3-E4
Revealing mistake: When Oliver meets Thea at the Grind and Jot Cafe (Which looks unsurprisingly like CC Jitters) you can see the cups on the table are from CC Jitters. (00:20:50)
Character mistake: They are in the interrogation room questioning the fiancé of the scientist Natasha when the captain says, "the blood we found at the scene of your fiance's murder, it didn't belong to Bobby Cordero." The characters name was Benny Cordero, which the captain says correctly a few lines later. (00:33:25)
Death at Victoria Dock - S1-E4
Character mistake: Fisher refers to some characters as speaking "a Slavic language." The characters are Latvian anarchists. Lettish (aka Latvian) is a Baltic language, not Slavic.
Continuity mistake: In the final scene, John Ross decides to drink some of the whiskey from the bottle that his father, J.R. Ewing, left for him. The bottle of whiskey is about half full, filled to just about the bottom of J.R. Ewing's signature on the bottle. As John Ross reaches for the bottle, it is now suddenly only about 1/6 full compared to the half full it was from the previous shot. The level continues to move up and down. (00:41:45)
Continuity mistake: When Lin lifts the rocks around the house in the final scene, there are eleven of them. But in the last shot, there are only eight rocks.
Continuity mistake: When Jeff Clarke comes by the firehouse, Hermann wants to hug him but Clarke says "I don't really like people touching me." But throughout season 2 Clarke has hugged other fellow firefigthers (Cruz among others) with no problem.
Factual error: Most of what Will says about the Challenger's O-rings is wrong. First of all, he says they are meant to keep hydrogen from leaking out of the SRB. SRB stands for Solid Rocket Booster, meaning they use solid fuel, not hydrogen. The hydrogen was in the external fuel tank. Second, the O-rings were tested for cold, and NASA engineers recommended against launching that day, with one of them even refusing to sign off on the paperwork if the launch was to go forward. NASA overruled them and went ahead with the launch anyway, with all the disastrous consequences that ensued.
Factual error: Chief Superintendent Hilton wears the ribbons of the General Service Medal (awarded for military service in a combat zone, most commonly in Northern Ireland) and the Police Long Service and Good Conduct Medal (awarded for twenty years' service), but not the Golden Jubilee Medal (awarded to all officers with five years' service in 2002), which he would also have. When he reappears in Series 4, he is wearing the Golden Jubilee Medal, Diamond Jubilee Medal (awarded in 2012) and Police Long Service and Good Conduct Medal, which would all be correct, but no longer has the General Service Medal.
Factual error: The battalion commander wears the correct crown and pip of a lieutenant-colonel, but the four cuff rings of a full colonel (lieutenant-colonels wore three).
Continuity mistake: When Buzz and Provenza race out of the squad room to follow Rusty in the frantic search for Stroh, Buzz is in shirt sleeves with no tie. However when they arrive at their destination Buzz is wearing a coat and tie.
Factual error: Noticed this watching season 2, and I assume it was also the case in season 1. The entrance of the Miramar Playa has flags from various countries flying. One of them is the Canadian flag with the maple leaf. Wrong flag. In that period the Canadian flag was the "Red Ensign", or "Dominion Flag." The maple leaf flag wasn't introduced until 1965.
Factual error: Whenever the Stars and Stripes is shown it is the modern 50-star version, not the wartime 48-star version as it should be.
Caleidoscope - S2-E4
Character mistake: The chess set in Dr. Pierce's home office is set up incorrectly. When the men are set up properly, each player has a light colored square in the right-hand corner. The board as it appears in the show is set up so that the light-colored square is in each player's left-hand corner. This "beginner" mistake puts the king and queen in the wrong positions.
Factual error: A plastic bag of items is found under the footboard. Plastic bags weren't invented in 1969. They first appeared in public in 1979.
Turtles All the Way Down - S1-E13
Other mistake: When Dr. Lee and Dr. Evans are arguing just after Red Reality Michael and Green Reality Michael converse, Michael turns around and says, "Shut up!" but the closed captioning says, "Enough!"
Revealing mistake: In the scene at the beginning when Scarlett is signing autographs after hers and Gunnar's small concert, you can see her signing a poster with a marker that doesn't leave any ink on the poster. (00:08:15)
Factual error: Thomas holds the Gendarmerie rank of Capitaine (by which he is frequently addressed by his subordinates), and thus should wear three horizontal silver bars on his epaulettes. However, in the only scene where his rank is displayed he instead wears the two chevrons of an ordinary gendarme.
Visible crew/equipment: When Rebecca Madsen jumps in her car to pursue the armored truck, as she does a U-turn and takes off at high speed, you can see all the people standing on the side watching the filming. Some even have their phone cameras out videoing it. (00:29:30)