There are many different reasons that chaos always develops.
First, all of those residents were warned to leave, many did not take it seriously enough, many could NOT leave due to sick loved ones or did not have the means (a car, trapped in their own home, etc.) Once the reality and weight of their situation hit them, then the panic started. Plus the fact that they were told to wade through all that disgusting water and try to make it to the Superdome for assistance...once they got there, there was none. They sat and waited in that huge cooking pot and the conditions only got worse.
As far as the "looting" goes....I can understand taking food and water, maybe even clothes...but the TV's and other such $ items does not make sense. You have no home to store all these stolen goods and you're going to be evacuated anyway, so what's the point? Bush says "zero tolerance for looters"...PLEASE....If he was down there, he'd be the first to cry and steal a row boat! The retail bastard Walmart will survive...trust me...it's the little mom & pop stores that will be forced to close due to the looting and flooding.