Okay, since Tsunade's about to be featured in the anime, I thought I'd see everyone's opinion about her.
Personally, I fall under the 'can't stand her' school of thought. She's got some serious character flaws that I feel make her completely unworthy to be Hokage.
First, her gambling problem. Now, the Hokage is supposed to be the village's leader, not necessarily a frontline fighter. Leaders are generally supposed to be reliable, honest and of good moral character. Tsunade has lied to the point of changing her appearance to run away from gambling debts, and there's certainly a suggestion that she's stolen her fair share of money in order to have money to gamble with. Where else would she have gotten that huge case of bills that shocked Shizune so much? Personally, I don't want a robber and debt-evader for my leader.
Secondly, her inability to deal maturely with grief. Yes, her younger brother and the man she loved died in battle and she couldn't save them. That sucks. It's sad. However, they died honorably, in battle during a time of war. They're ninjas, that's what happens in war time. Yes, it does place a burden of guilt on her that with her medical skills she couldn't save them. However, all doctors, ALL of them, have to deal with patients dying. If you're a combat field medic, and half of your patients die, you're ahead of the game, no joke. Tsunade by this time was a mature ninja, not a child, and should be expected to be able to deal with both grief and survivor's guilt. To become so non-functional that she not only can't be a medic, or even a ninja at all, is showing a lack of coping ability, but becoming so freaked that she can't even stand to see blood is completely uncalled for.
Grief is difficult and trying, but it's also part of a coping process, and adults should be able to deal with grief and move past it, even when dealt very heavy blows, most especially when one is a ninja and death is an accepted part of living as a ninja.
Look at Kakashi: he admits to Sasuke that everyone he held precious to him is already dead, yet he continues to do his duty to the village, completing missions as a jounin, training students and even protecting Sasuke as much as he can. His teacher died, his best friend is on the memorial and one assumes his teammates also died, so he had no one obvious to lean on during his grief, yet he still continues to do his job and live his life. Tsunade, on the other hand, still had teammates and a teacher who would have helped her cope. Jiraiya seemed to care about her wellbeing, and the Third was very kind, so she wouldn't have been alone in her grief.
So, let me hear your thoughts.