Mmm, this subject makes my head hurt.
I don't see why paradoxes and plot holes should stop you from writing a time travel story. Heck, enough people have done it already, and they sure as hell didn't fix those problems. ^_^
I'm partial to the parallel universe/timeline take on time travel. That is, when a person time travels, they don't travel into the past of their current timeline- they travel to (or create) a new timeline. The timeline they travelled
from (their "original" timeline) ceases to exist. Additionally, they can't
recreate their original timeline exactly, as you can't replicate events (take one unexpected step to the left and you've already altered the way things panned out in your original timeline).
As soon as a person creates or travels to a new timeline, they have the opportunity to take another shot at the future. Thing is, though they've escaped the future of their original timeline, they still can't predict events, because the very act of replaying the timeline is going to change how things happened. All they can do is hold on tight and hope that their future in this timeline is less buggered than the one from their original timeline.
I also think that time travel should not be readily available. If it's difficult to time travel, people won't do it for any ol' little reason. That means
not being able to go back 6 hours into the past to avoid eating that chicken burrito.
