Thanks to a mandatory 6-hour online defensive driving course, I've taken the copious free time included in that timeframe and the poor judgment of a friend who already bought Hancock on DVD and have finished getting through it playing in a tiny window in the background while I complete the course. This was spurred by the overabundance of extra time included and a commenter on Jeff's counter-Hancock post asking about the differences:
In the first ten minutes, there's a character-building scene that expands Hancock in the bar early on. Readers of the original Tonight, He Comes script will see a piece of the movie that would have been preserved here. He meets a girl, she comes back to his place, and Brodie Bruce's (from Mallrats) curiosity about "when that moment comes" when Superman and Lois Lane are intimate is explored.
Both watching it and checking other sources, the only other difference I can find is the means of transportation used to get to Hancock's trailer a little over an hour in to the movie. It's an alternate shot choice that then causes a continuity error.
The additional scene is definitely an improvement over the theatrical cut, but it doesn't change how far off the rails the movie goes in Half Two. If you haven't seen it, the opening add-on is nice, but doesn't make it worth your time.
The performers do good work relative to what they're given to work with, as does Berg, but the plot is what it is. For those who felt this movie really subverted the superhero genre in any way, you really should read the original script. It was much more adult and less "A La-La Land Superhero Story".
It doesn't ignite a revolution when there's rampant cursing and alcohol abuse in a superhero movie. If you haven't seen it, catch it on cable when drunk yourself or wait for someone who doesn't know any better to throw it on in a "hey, let's watch this" when you have an escape option if it loses you halfway in like it did myself and others.