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)
Plot hole: If the Lady of the Lake walks every night to her room and kills those in her path, why didn't Flora and Miles' parents die in their room by the hands of the Lady in the Lake when they first moved in?
The Funeral - S1-E3
Deliberate mistake: Though it serves the drama and black comedy of the scene, it's highly unlikely a modern, let alone future broadcasting network would neglect the importance of delay (usually around 30 seconds) between recording and "live" broadcast. Specifically, to prevent unexpected gruesome incidents like the exploding head seen in this episode from making it to air.
Opening Act - S1-E4
Factual error: At the beginning, the screen shows that the year is 1988 in Corpus Christi, TX, then the camera pans into Selena and her sister eating tacos when their friend Jake arrives wearing an Arizona Diamondbacks shirt. The Diamondbacks did not exist in 1988. Phoenix was awarded a Major League Baseball expansion team in 1995 and the Diamondbacks made their debut in 1998, 10 years after this scene takes place. (00:00:30)
Continuity mistake: In early versions of the episode, Luz is shown wearing her Hexside school uniform before she even receives it. This mistake spoils the ending. Fortunately, it was fixed later on. (00:00:01 - 00:00:40)
Visible crew/equipment: The camera crew and camera can be seen in the far left user box during the virtual meeting on the laptop. (00:16:00)
Factual error: The communication delay for earth-moon communications is around 2.6 seconds. Yet Emma's daughter simply dials a cell phone and is connected to her Mom in space past the moon in less than that. The communication has no time lag. (00:18:45)
Plot hole: Dr. Adam Soong is initially presented as a discredited scientist, banned from the scientific community; he gets debarred and his funding revoked. And it's not an internal matter; he is publicly exposed for it. His daughter in episode 6 even finds out this information on Google. Several news articles call him "mad scientist" and such. However, this same person at the same time throughout the rest of the season has every bit of pull and influence, not just through undercover channels, but is treated with the utmost honor and deference by the NASA PR people at public events.
Continuity mistake: Kurt is still recovering from the beating he took in the previous episode with bad cuts on his forehead, checks and temple area. They are red and impossible to miss while he is in the police station. The cuts have miraculously disappeared in the next scene when he goes to visit Mona.
Character mistake: The FBI team responds to a murder crime scene. The victim is lying face down in the bed with blood everywhere. The team leader takes the victim's wrist with his bare ungloved hand. A trained FBI agent would never touch a murder victim without gloves - one to protect himself and two not to contaminate the crime scene. (00:10:00)
Factual error: The show, which is set in California in 1947, mentions the gas chamber, lethal injection and the electric chair as methods of execution in the state. Two murderers are sentenced to death by lethal injection and one is depicted being instead executed in the electric chair, which the governor states has been brought out of retirement for the occasion. In fact, California adopted the gas chamber as its sole method of execution in 1937 (having previously used hanging). Lethal injection was not used in the United States at all until 1982 and not adopted in California until 1993 (becoming the prime method in 1996). California has never used the electric chair.
It's Good to Be Back on the Moon - S1-E9
Factual error: The Apollo 11 flag gets knocked over by the Chinese rover...but the flag was blown over by the Eagle's takeoff thrust, witnessed by Buzz Aldrin. This was confirmed years later by the Lunar Reconnaissance Orbiter, which showed shadows of the flags planted at all six Apollo landing sites, bar Apollo 11's. The other 5 were all planted further from their landing craft precisely for that reason. It's also widely assumed that the flags on the moon would have been bleached white by decades of unfiltered sunlight, not in good condition like the one shown.
Other mistake: At the end, when the reflection of burned Lucy still shows her beautiful, Dracula's reflection shows him as he is seen; not old and ugly as in his usual mirror reflections.
Continuity mistake: An employee is asked to leave the computer lab, he actually exits it twice. (00:11:15)
Factual error: Emily is in Paris when her boyfriend calls from Chicago and wakes her. She asks the time which he says is 7pm, and she says 3am in Paris, which cannot be. Central European Time is 6 hours ahead of NY and 7 from Chicago. 7 pm in Chicago would be 2 AM in Paris.
Continuity mistake: When Gi-do is checking himself into the hospital, he flips up the sunglasses he is wearing. The shot then cuts to Haeng-ja whispering something to him, and we can see Gi-do's right hand raised to be level with his head. When the shot cuts back to Gi-do, his right hand is suddenly lowered. (00:31:02)
In Dreams Begin Responsibilities - S1-E1
Continuity mistake: She is on an elevator wearing her uniform. The uniform collar does not show her Chief of Police stars on it but when she walks off the elevator down the hall into her office less than 10 seconds later, the stars reappear on her collar.
Factual error: Paul tells Shea that he has a condition called Sporadic Fatal Insomnia. Later, Shea finds a fork in a bag labelled Abby. Paul explains that Abby is his daughter, and he wants to test her DNA, because she has a 50-50 chance of contracting the disease. This is false. Sporadic Fatal Insomnia is not hereditary. Fatal Familial Insomnia is genetic and is the inherited form.
Chapter Five - S1-E5
Factual error: Pete uses the term "throwing shade" when talking to Perry Mason in the middle of the episode. As this show is set in 1932, the phrase "throwing shade" did not yet exist (the phrase was first introduced in the 1990s). (00:35:00)
Suggested correction: The phrase was not first introduced in the 1990's. While it did become popular in the 1980's, the idea of "throwing shade" as an idiom would have been around before then. A variation of the idiom is found in writings from the 1800's, for example "Mansfield Park" by Jane Austen.
Continuity mistake: The three friends finally meet in person after all the texting. Karube brings a cigarette to his mouth when Chota asks "Where to?", but in the next shot his hand is lower. (00:07:15)