one thing that Tsunade mentioned is that Danzou led a hard-line faction during the Third Hokage's era, but that that faction had collapsed... DB's very questionable translations say that, although Danzou was able to found the Root division of ANBU (which he commanded): "Root has been disbanded, and he (Danzou) has already fallen into disgrace".

Now, regardless of the confusion about Root being disbanded or not (i mean, they just said that Sai is from Root, and so you imagine it's not entirely disbanded...) this pretty clearly implies that Danzou's power and political reputation in Konoha is less now than what it once was. So, considering this, it seems Danzou didn't have the support to be seriously considered for Hokage after the Third died...

I don't really know... but Tsunade's reference to Danzou's hard-line party losing power and him being "in disgrace" makes me wonder if his downfall might have had something to do with the important events in Konoha history that we know of (the Uchiha massacre, the war against the Sand, the war against the Thunder, Orochimaru's defection).