Here's the Deal with the Clock. Since the Pats had to go for it on forth down and trhe pass was incomplete as soon as the Ball fell from Moss's hands and wnet as an Incomplete, the play was dead and the Clock had to be stopped. However, When people started storming the feild, the time official just ran the last second off, which actually should have been two seconds.
Either way, if your the Head Coach of a team, you should be on he feild everyplay, regardless of whether or not that last play will make a difference. It may have been classy for Bill to go for the end of game hug, but when the game was restarted, he should have stayed.