I agree, it is a great plot for someone like my wife who will take in a good character story, and be willing to not think through the details. For people like me who enjoy seeing how the plot details make sense, there are a lot of roadblocks with this one.
Just a fair warning that I am not gonna use spoiler bars anymore. I figure everyone who has not watched the film yet has not made it this far down in the thread.
As far as my hand shoot theory goes, I assumed that powerful enough memories that were newly created would be soon after remembered and take by the person sent back. That's why old Joe remembered that hot steamy farm house lovin' young joe had. Other things like smashing the watch and going back into town pop in as well. My thought is, Joe shooting his hand would lead to the gun dropping, old Joe going "WTF happend to my hand??", and hopefully in that time, Sara would pick up the gun. Then the memory of young Joe realizing how the rainmaker came to be would surface on old joe and he would give up the chase at that point.
I could be wrong though. I was making assumptions. I assumed young joe wanted to see the picture of old joe's wife as an attempt to overwrite his memories on him, and that is the same reason old Joe wouldn't let him see it.