All the World Is Birthday Cake - S2-E5
Corrected entry: Everyone on the planet freaks out because two of the crewmembers have birthdays soon, marking them as "Gilliak." But no-one makes the connection that birthdays, dates, years, etc. will be entirely different on this planet than under Union dating.
Virtue of the Vicious - S1-E10
Corrected entry: Karen had her gun taken away before the interview. We even see her search for it and realise she doesn't have it after the bomb goes off interrupting the interview. At no point did she have the opportunity to get it back before being taken hostage afterwards, but then somehow has it back in her purse to shoot Luis in the foot.
Correction: Karen does not use her gun to shoot Lewis, she uses the gun she picked up from the dead Anvil agent in the room.
A Crisis of Faith and Octopus Aliens - S2-E3
Corrected entry: The episode is set in 1989, but they discuss the movie Ghost which did not come out until 1990.
Correction: Not necessarily; since the second season has begun, they could have progressed to 1990 by this point. It also hasn't been established whether he's had his tenth birthday yet at this point in the series.
Sheldon's birthday is Feb 26, 1980.
I knew his birth year had been established already on BBT; I just didn't know for sure if the date he had a birthday within the parent series corresponded to the "real" world because BBT time only roughly coincides with real-world time in most cases.
While a BBT season may not be a full year or the next episode isn't set one week later (like many sitcoms), because the show relies on pop culture so heavily, like releases of films, etc, I do think BBT is set in the real life timeline, even if a holiday special is set in the "future" (e.g. a Halloween episode is aired 2 weeks before Halloween.) However, with YS being set in the past it can be hard to tell what the exact date is, unless specifically said, and you have to rely on context clues (like a lot of shows set in the real life timeline past). I only replied with his birthday so others could make a decision if the correction is valid. I do not know enough about the episode to know when it's suppose to be set or how long it's been since his birthday (as I did think he was suppose to be 10 in the episode).
Corrected entry: As the hologram of Captain Maddox walks toward Burnham, it steps up the steps, complete with reflections on the floor. Maddox would be in a hologram projection chamber with no steps, let alone a reflection, and no steps.
Correction: First of all, there is nothing in the show that indicates "projection chambers" are used. The holograms appear to be generated from bridge so any interaction would match the room they are in. As for the reflection, the hologram doesn't produce the reflection. The floor is reflecting the hologram.
Corrected entry: Marty tells Dell that he never told his wife anything about what he does in money laundering. In later episodes it is revealed that he tells his wife everything. In fact, she becomes his accomplice. (00:31:00)
Correction: It's not a continuity mistake if he was lying. He lies throughout the show.
He's lying to protect her.
Corrected entry: The tombstone of his wife says Dec 15, 1988 to Oct 15, 2018 which makes her 29. Their daughter is 17-18 which put her at 12/13 when they had the oldest daughter.
Correction: The date on the Tombstone is Dec 15 1983. Which makes her 34. Emma is 16/17 as she is about to leave for college, which puts the age Alana gave birth to her at 17/18 which is not that unrealistic.
Corrected entry: You would not have to fly over the Himalayas when travelling from New York to Anzhou (near Beijing). You would go the shorter way round the globe.
Correction: In practical terms, that might be true, but the whole flight was a setup.
Correction: While I agree the premise is a bit shaky, my understanding from watching the episode is that the people of the planet had it so ingrained in their culture, they weren't willing to consider that. Regardless of where someone was born, if they were born during the period of that sign on their planet, they were under that sign. While watching the episode, I hoped Captain Mercer would use your logic to free them, though. He could have simply said "You know what? We have that same sign in our culture, but because the stars are different for us it comes at a different time."