Pfft. Assuming our understanding of quantum mechanics is correct, it's not possible to change the past if you go back in time. (Note: neither quantum mechanics nor relativity rule out the possibility of time travel, just that of changing the past) A time-traveller would only be able to do things that he already did in that time (by `he', I mean the time-traveller returning to the past, not the version of him that already existed at that time (although he would also only be able to do things he already did, because he already them, if that makes sense)). Paradoxes don't and can't happen, and any attempt to cause one will fail.
Also, all current theoretical time-machine designs have the constraint that they cannot send a person back to a time before the time machine was constructed (which is obvious if you think about it, since the time machine doesn't exist anymore).
If I had the chance to go back in time and watch/relive history, then I would want to observe the following:
* The supposed Roswell UFO crash incident of June/July 1947
The object that crashed near Corona, New Mexico has been identified as Mogul Flight #4, a high-altitude balloon designed to detect Soviet nuclear tests. The project was Top Secret at the time, which is why the wreckage was shipped to the Roswell Army Air Field and the alien spaceship story was created as a cover-up. Apparently the cover-up worked too well, since people
still believe it was an alien spaceship, even after all the details have been declassified.
* Find out what happened regarding the death of Elvis.
He died of a heart attack, possibly brought on by drugs, on 16 August 1977. What else do you want to know?