I admit that I don't know much about the theory of relativity, but there's one point I wouldn't mind have clarified:

If you have a watch to keep your own time, and you travel away from earth fast enough to experience your own unique rate of time passage, then return to earth after measuring 72 hours, will you find that the earth has rotated 3 full times?

You talk about traveling fast enough to experience a unique rate of time passage. Everyone has their own unique rate of time passage at any speed relative to someone else. So if your watch shows 72 hours have past, what someone else's watch shows will depend on your speed relative to their's. For ordinary speeds far less than light speed, this difference is extremely small. It only becomes significant at speeds a significant fraction of light speed. The equation for time passage relative to a stationary observer is
T=T₀(1-v²/c²)^{1/2. Here, T is the time you measure while traveling at a speed v relative to a stationary observer. T₀ is the time measured by the stationary observer, and c is the speed of light. So if you are travelling at 1/2 lightspeed relative to the stationary observer, after 72 hours have passed on your watch, about 84 hours have passed on his, that's 3 1/2 orbits, and you've bought yourself 12 hours worth of longevity.}

Gerry, has the person traveling 1/2 the speed of light actually gained 12 hours, or is the difference only true from the point of view of the stationary observer?

Good question. Everyone has their own measure of time depending on their speed relative to something else. With the traveler traveling at 1/2 lightspeed, and at constant velocity (no force, no acceleration), relative to the stationary observer, there is absolutely no way he can tell whether he is moving away from the observer, or if the observer is moving away from him. Consequently, while the observer sees the traveler's time passing more slowly than his own, the the traveler sees the observer's time passing more slowly than his own time. Both are correct, all time in non-force motion is relative, they each correctly measure their own value of time. It is only when the traveler meets up again with the observer....and he must change his direction of motion and/or speed to do so, which requires a force and an acceleration...that is, he undergoes force motion...then at this point when they compare watches, the travelers watch shows 72 hours elapsed and the observers shows 84. The traveler ahs travelled into the observers future, and has aged 12 hours less than he would have aged had he not chosen to go on his journey. But time has passed completely normally for both during that trip, there is no way to make the comparison until the return.