There are term limits for a reason. Bloomberg was a megalomaniac who didn't want to follow the same rules as everyone else. He should not have changed the law simply so that he could stay in power. His overreaching political style was bad for New York, and his legacy today is a bad one.
Mayor Bloomberg overturning the term-limit law in New York is not justified. Bloomberg pushed the bill through quickly and late at night when no one was paying attention because of the national elections. He did not consider the desires of his constituents. The people of New York had previously voted on and accepted two referenda in favor of term limits, so I think that this makes it very unjustified for Bloomberg to do what he did.