Katrina is probably mishandled by Dean, and the economy still goes in the tank, as the recession was probably on the books since at least the 70s. Dean probably tries to pull out of Iraq sooner than OTL and without getting the Tribal Chiefs on the gvt. side first, meaning there is probably chaos but less American loss of life.
He would not however try to reform Social Security.
So his approval rate by 2008's election would be very low, but perhaps not at the level where he is guaranteed to be blown out.
I think that the Left would become disillusioned with him by 2006, as he would support Israel's war with Hezbollah, and he wouldn't cut and run from Iraq as quickly as they wanted him to.
Its worth discussing however, his absence as head of the DNC. His tenure was very successful in getting a lot of moderate Democrats elected and taking over Congress. Without him organizing the 50 state strategy, the Democratic Party is going to have difficulty winning elections for the same reason they do so poorly at the lower levels right now, and that is a lack of organization and an unequal distribution of fundraising.