...For that matter I assume it isn't taking into account acceleration (note to physicists: does non-gravity acceleration cause time dilation?).
Still it is free, and makes me feel very very very slightly younger!
IAAP (I am a physicist), so I can confirm that non-gravitational acceleration causes time dilation, under some circumstances. Since I'm waiting for some calculations to finish running through Mathematica, I'll also try to explain.
Non-gravitational acceleration does cause time dilation, at least when viewed in the frame of the accelerated observer. When analyzed in the frame of an inertial observer (read: if someone who isn't accelerating calculates how much time has passed for you based on how you are moving), these effects appear to be the result of your velocity, and *not* your acceleration.
A fun example of this is the Langevin twin paradox problem. Two twins, floating in space, synchronize their watches. Then twin A uses a rocket to travel out a certain distance d at a more or less constant velocity v, turn around, and return, also with velocity v. He only uses his rocket for a very brief period upon leaving, during turnaround, and finally to return to rest relative to his twin. Twin B just sits there. They then compare their clocks.
Twin B sees that twin A spent essentially all of his time moving with velocity v, and figures that time-dilation has caused twin A's clock to record less time than twin B's. This is correct.
From twin A's perspective, it was twin B who moved with velocity v, and so he figures that time-dilation has caused B's clock to record less time than A's. This seems paradoxical until twin A accounts for the fact that he was accelerated at the far end of his trip. During that acceleration, everything not attached to his rocket (including twin B) seemed to accelerate in the direction his engine was pointed. There's a bunch of math one can do to justify it, (see chapter 13 of Misner, Thorne, and Wheeler's "Gravitation", if you want the full scoop) but the short version is that acceleration acts just like gravity (and vice versa). So twin A figures that twin B's clock must be gravitationally blueshifted relative to twin A's clock (twin B is 'higher' in the apparent gravitational potential produced by the acceleration). It turns out that over the amount of time twin A must accelerate to return to his twin, twin B's clock seems to gain exactly twice as much time as he seems to lose while twin A is coasting, which is just enough to bring each of the twins' calculations into full agreement upon their reunion.
Relativity is fun.