40 extra minutes in a martian day definitely make things interesting. Going further, how will time work when we're stationed around Saturn's moons? We will probably need some universal units of time that work regardless of how long it takes you to rotate around the sun. (Stardates?)
Seconds since epoch is good enough for almost all purposes until you're moving at ~10% of the speed of light; they'll be fine for computer timestamps as long as acceleration and deceleration are gradual. So I don't think we'll need any new universal units of time, only new local units of time, and I'm not even sure about that. For mars, just extending the day until 24:40 = 00:00 seems reasonable enough. For Saturn's moons the sun is faint enough that keeping "earth time" is probably reasonable - whether it's solar day or solar night will make very little difference to most people's lives, I would think.
