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)
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)
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)
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)
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: Throughout the series, the Barbers pull their cars straight up their driveway. But the cars are nearly always shown coming back down the driveway driving forward.
Continuity mistake: When Elizabeth says "Do you mind if I lie down in your guest quarters?" Jamie's hands are down by her side. The shot changes and one of her hands is now up by her face.
Facing Fear - S3-E4
Factual error: The teams are at a US Coast Guard base. Two coasties are introduced. One as a chief (correct) and one as a "Captain." He is not a Captain, he is a Lieutenant. The USCG uses naval ranks, so the person with the two bars is a Lieutenant. A Captain is three pay grades above this, and uses eagles as insignia.
Continuity mistake: The background characters passing Fredwyn and Janice disappear in one frame, and then appear in the next. They also seem to randomly speed up and slow down in the background. (00:20:37)
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.
Revealing mistake: There are bullets placed on the counter, the one casing has a hole in it from being drilled to show it's a dummy round and there's no gunpowder in it. (00:14:45 - 00:15:20)
Other mistake: A police officer is shown at a hostage scene. He has Sergeant stripes on his sleeve, and Captain's bars on his collar. He is one or the other. But not both. (00:11:50)
Factual error: In Massachusetts, Atticus, Leti and George are attacked by the local sheriff and his deputies, who are patrolling the county roads. In Massachusetts, sheriffs run the county jails, but they do not (and did not) handle routine policing, which is the responsibility only of municipal police departments.