In The Undiscovered Country, there's clocks on the bridge which correspond to the ship's clock. I've always wondered what that clock is set to?
If you say it's a day of the week, then the ship's date and time are presumably set to a coordinated time set throughout Starfleet. But what would that be? Is it set to the time and date in Paris (the Federation's seat of government)? Or to Greenwich Mean Time (GMT)? Or Pacific Standard Time (since Starfleet Command is in San Francisco)?
Then you throw in that Deep Space Nine uses a 26-hour day. So a Tuesday on DS9 might not mean it's Tuesday aboard the Enterprise for events occurring concurrently.
A bit late to reply, but something similar happened in World War I and World War II in the battles of the Atlantic and Pacific.
When German warships sailed, during World War I, they used Berlin time as their basis of coordination, which was two hours ahead of the British fleet, which used Greenwich mean time on their ship's.
When compiling battle logs for the Battle of Jutland, the German records are always two hours ahead of the British.
For the British, first contact with the German fleet occurred at 14:30 on May 31st.
German records put first contact at 16:30 on May 31st due to the two hour time difference.
In the Pacific, the Japanese calendars and clocks were always a day ahead of the US navy, because of the International Date Line, and the US Navy used a combination of Hawaiian time and local time to coordinate their efforts.
To the Japanese people, Pearl Harbor is remembered as falling on December 8th, not December 7th.
Prior to the October Revolution, the Russians during World War I, used the Julian, as opposed to the Gregorian calendar, meaning they were 13 days behind their allies on the Western front.
