I think Harry needs to grow up. He's third in line for the throne and needs to show some responsibility. It's great that he apologised, but ridiculous that he did it in the first place. Having gone to one of the most prestigious boys schools in the UK, he should have at least picked up on the fact that the Holocaust was a bad thing and it would be in poor taste to wear an SS outfit or swastika at any time.
Had he been any other rich young man at the party, it probably would have been overlooked. But fact is, that he's not. He's in the public eye, whether he wants to be or not. His brother William realises this, and went as a lion (as well as apologising publicly for Harry's choice of costume).
Apparently his wasn't the only bad taste at the party though, as some girls went in blackface.

What makes these rich kids (because the majority of them certainly aren't acting like adults yet) think they can live without any sense of social decorum or decency is beyond me.
But on a positive note, both William and Harry volunteered for the British Red Cross this week to help the tsunami effort. And it's thought that Harry will be asked to take on more public responsibilities until he begins at Sandhurst (delayed his entry because of a knee injury).