Although Patty seems to have responded failry eloquently, I would agree that her original "I bet you never noticed" comment was meant to convey "I bet you never noticed that Ben Tolpin had to be replaced in the middle of the production
and that most footage with him had to be reshot with Brandon Stacy but that a few over-the-shoulder shots are still actually Ben's shoulder." I think she's probably right: Ben Tolpin's Spock footage was pretty neatly excised without viewers being any the wiser. I bet most people can't see the seams.
Yes, ships travelling at sea traversing muliple time zones maintain "ship's time." In my cruise from New York to Halifax, the ship stayed on EST even when we were docked in Halifax, even though Halifax was on Atlantic Standard Time. Also, as Patty indicated, the International Space Station "resides" in GMT--despite traveling over all 24 time zones in the space of about 90 minutes.
For what it's worth, Spock indicates in "The Conscience of the King" that the Enterprise will be arriving at the planet Benecia at about "1500 Benecia Time." So evidently for some purposes, an an entire planet has some agreed-upon time.
I'm not sure the U.S. Navy would agree with the notion that everyone should just work "their own day" while on board ship. That seems kind of chatoic.
I think Starships are probably like Intensive Care Units: they don't sleep, but there's an important diurnal ebb and flow that it's best to maintain.
Concerning Ben Topin: I noticed. No complaint, but I noticed. The idea that your viewers didn't notice is bizarre.
Concerning night and day on earth: The interpretation of the statement is bizarre, since it's always every hour of the day somewhere earth. I understand that comment to mean that the Enterprise followed a 24 hour day, with 'time off' following the idea of night and day on earth, rather than the human clock which is not exactly the same as the 24 hour day. People living in dark caves cut off from the cues of the outside world do not follow a 24 hour day. Right now Kirok L'Stok is in the early morning hours of March 1, while I am in the late afternoon hours of Leap Day. It's not even the same DAY everywhere on earth, for Pete's sake. There would be no logical reason to undercut efficiency in deep space during certain hours by declaring they are to be 'night' for the whole ship. Everyone can work during their own day, every shift. Falls into the whole, "Why I am not such a great Trekkie" class of statements. I like Trek, I love Trek Fans. I'm a Trekkie Fan!
And yes, I live in New York City... I can order a breakfast or dinner at any hour of the day or night. It would only make sense that a large Starship never sleeps...