Actually, movement in WHICH coordinate system? ('Chart' lest someone objects to my using the wrong terms again.) Most of these ideas presuppose that there is some fixed point, and the Earth moved relative to that. But the whole point of special relativity is that fundamentally there is no preferred frame. Well, not among inertial frames, at the very least. The frame of the railway station and that of the train going 100 mph past it are equally good.
General relativity has you deal with acceleration and is a bit more of a pain in the rear, but basically still, you can transform between almost any two frames. Well, as long as you don't have some coordinate singularity, like going through an event horizon.
But anyway, even presupposing a preferred frame, i.e., basically a fixed point in the universe... are you sure it's that easy? What movement do you take into account? Just Earth around the Sun? Also Sun around the centre of the galaxy? Galaxy in relation to the local cluster? The dark flow towards the Great Attractor? Universe expansion, if that point isn't pretty much on top of us?
(I mean, bound systems move in relation to where the 'here' coordinate would be a million years ago. Think two treadmills put front to front, running in opposite directions. The 'you are here' point moves away from the centre over time. But if you put two footballs tied with a rubber band to each other on that system, they stay at the same distance from each other. Essentially they both move relative to where their respective previous 'you are here' point was.)
Or are you sure that for time travel over really vast time intervals, you even know every asteroid that passed close and gave Earth a wee bit of a gravitational nudge?
Now some of those corrections may or may not be small (I expect the Hubble expansion one to be really negligible at these scales, for example), but you don't need to miss that mark by a lot to end up dead anyway. E.g., you just need to end up 10 ft (3m or so) underground with your DeLorean at 88mph to be dead.
Granted, that IS thinking it through a bit further through than Emre apparently did.