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It's not just time zones and leap seconds. SI seconds on Earth are slower because of relativity, so there are time standards for space stuff (TCB, TGC) that use faster SI seconds than UTC/Unix time. T2 - T1 = [God doesn't know and the Devil isn't telling.]
If you run a realistic physical simulation of a star, and you include every subatomic particle in it, you’re going to have to use very small time increments. Computers can’t handle anywhere near that many particles yet, but mark my words, physicists of the future are going want to run this simulation as soon as we have the computer to do it. Also, the simulation should predict events billions of years in the future, so you may need to build a new time tracking system to handle that.
Good point. You'd need at least 215 bits to represent all measurably distinct times (in multiples of the Planck time, approximately 10^-43 seconds) out to the projected heat death of the universe at 100 trillion (10^14) years. That should be sufficient for even the most detailed and lengthy simulation.