I can't think of a single moment off hand that sticks out, although the name Mike Tyson is one of the first things that come to mind, but I'll come up with a specific one.
This one is not a single moment because it usually lasts about 3 hours but it is painful to have to go through an entire NFL broadcast where Dick Stockton does the play by play. Now Dick is not loud, or particularly obnoxious, but he is famous, at least in my family, for the extraordinary number of mistakes that he makes every game. We keep a little tally sheet for fun on Dick's boo boo's, and if he gets into double digits by halftime we all celebrate (for Dick) by having triple shots of Tullamore Dew. Needless to say, we always root for Dick to hit that halftime target, and we are seldom disappointed.
I know that this relates to the athlete or sportscaster's worst moment, and I hate to bring it up, but for me personally the worst sports moment was also a halftime of football, the second half of the Sugar Bowl. I can not remember a more disheartening 30 minutes of football. It was like watching something, but not really believing it was happening. Needless to say, after that game, the Tullamore Dew was used for more than just the Dick Stockton celebration.