He made a questionable appointment. Everyone makes mistakes. Sandra Day O'Connor anyone?
Law and Order: His law and order record does not go well beyond clearing the streets of squeegee men, bums, and hookers. Some tout his efforts to go after organized crime, but he lost all credibility on that when it was exposed that he'd appointed a corrupt high school dropout with mob ties to be the Commissioner of the New York Police Department. Bernie Kerik, again. Giuliani went on to strong arm President Bush into appointing Kerik to one of the top law enforcement positions in the country - the head of the Department of Homeland Security. Kerik had to withdraw his name when he was later indicted for his crimes for which he received an even later conviction. He avoided jail, but narrowly.
How about Souter? That may be the worst one of all time!