Re: What are the relativistic effects of the Earths movement.

You're exactly right about movement causing time dilation, and you recognize it's all relative.

There would also be a small time dilation effect if somone was watching the Earth from an extra-solar perspective. There's no such thing as a uniquely "fixed point" to watch the Earth from, but from any frame you picked, there would be a varying time dilation as the Earth changed its velocity as it orbited around the sun (or, for that matter, as the sun rotated around the galaxy). The size of the effect would depend on the total relative velocity. If another clock is moving (with respect to you) at some velocity v, that clock will appear to be running slower than your own clock by a factor of gamma, where:
gamma = 1/(1 - v^2/c^2)^0.5 (and c = the speed of light)

More relevant to everyday life are tiny deviations in the clocks of the Global Positioning Satellite (GPS) system. Here's an interesting discussion of these effects.