Historically, time-keeping has been a hassle for large empires on Earth. Different seasons, different time zones – all kinds of hassle. Now imagine an interstellar empire. Heck, just imagine a culture that exists on two or more worlds!
With artificial habitats and ships throughout the Solar System, the problem is simple. Everybody is on Greenwich Mean Time, a day lasts 24 hours and 7 days is a week; a year is 365.25 of those days, regardless of how long it took your personal cylinder of metal to circle around the sun. See you all at the pub.
Interject a planet with an environment that the residents have to interact with, however, and differences immediately begin to add up. Take Mars for example. If the first colonists (let’s call them Muskies, like Greg Benford http://www.strangerviews.com/books/war-dogs-greg-bear-book-review/ ) land on Mars on January 1, 2040, they’ll make camp and begin a day that is, generally, 24 hours and 37 minutes long, or 41 minutes longer than Earth’s 23 hours and 56 minutes. As the days goes by, the Muskies will fall farther and farther behind Earth. In fact, they’ll wake up around February 4, and it will be in fact February 5 on Earth. On March 9, it will be March 11 on Earth. (NASA mission controllers for Mars probes have a fascinating system for dealing with the problem but it is not one usable in the long-term. https://en.wikipedia.org/wiki/Timekeeping_on_Mars). Other celestial bodies generate even worse problems.
Some science fiction writers have turned to a “metric” or SI solution of using the kilosecond (I just finished reading Paul MacAuley’s In the Mouth of the Whale, http://www.amazon.com/Mouth-Whale-Quiet-War/dp/0575100753/ref=sr_1_1?ie=UTF8&qid=1439907850&sr=8-1&keywords=In+the+Mouth+of+the+Whale and the characters use this scheme). The second is a fixed, known period of time (roughly 9 billion vibrations of a cesium-133), and time-units based from there would be certain. Under this definition, a day is 86.4 kiloseconds, and a month is 2.3 megaseconds, for comparison.
A character living with such a system would say to his friend, “Do you remember that book I loaned you two megaseconds ago?” “Grandma lived to be 2.5 gigaseconds (78 Earth years).” Dates would be set by megaseconds from a fixed date: “Today is 1 kilosecond, and 1449 megaseconds After Moon Landing.”
Here’s the problem for the author and the reader: it’s hard! When a character says, “X was two weeks ago,” you know exactly what they mean. When they say something was a megasecond ago, you have to stop and do a quick calculation in your head. It brings the narrative to a screeching halt. It breaks up the flow of the dialogue or exposition, and may leave your less-than-hard-sf readers a little queasy.
On the other hand, a character living on an extrasolar planet, with a different rotational time and different length of the year, can’t simply write “July 5, 2042” on their checks. That doesn’t even mean anything in the context of a world where the day is 28 hours and a year 36 of our months long.
So which should it be, gentle readers?