Someone once told me that Prince Harry's grandfather, the Duke of Edinburgh, asked what advice he would have for a future Prince Consort, said, "Never stand when you can sit, and never miss an opportunity to relieve oneself."
To this we can add, "Don't be photographed wearing a swastika." When I was in local politics, a similar rule was, "Don't be photographed with a drink in your hand." Unless it's vodka, which doesn't show.
Third in line for the throne, all Prince Harry ever had to do was look pretty and avoid major embarrassment. This he was either too dumb, too undisciplined, or too miseducated in royal diplomacy, to manage.
In an ordinary wastrel, wearing a Nazi uniform to a costume party with no intent to send a political message would be no more than a sign of callow youthfulness and political ignorance. In an English prince, it's enough for a minor scandal.
It's conceivable that Harry is imitating his namesake from Henry the Fourth, Part One, who uses his reputation as a rakehell to disguise his ultimate political goals:
Yet herein will I imitate the sun,
Who doth permit the base contagious clouds
To smother up his beauty from the world,
That, when he please again to be himself,
Being wanted, he may be more wonder'd at,
By breaking through the foul and ugly mists
Of vapours that did seem to strangle him.
The notion that Prince Harry should be forced to take "Holocaust lessons" or do penance at Auschwitz, is offensive and stupid. It's just another example of exploiting the slaughtered. Our time is rife with them. We need no more.
Update: Interesting post by Roger L. Simon, and a long discussion afterwards, mostly about whether the monarchy should be abolished.