I'm sorry, but Harry was in his private hotel room!! He was in a suite to which he controlled access; it was not a public place. If I invite someone I meet into my house, does it suddenly become a public place? No it bloody well doesn't.
Why on earth should Harry be dishonourably discharged? He invited a couple of, it now appears, totally unscrupulous money-grabbing women to his room for a private party. He clearly didn't know just how disgusting these women were when he invited them up and I'll bet he regrets it now. While there he did nothing illegal or immoral. People have been getting drunk and then getting naked in one another's company since the dawn of time.
If an off duty soldier, most likely on leave ahead of a tour of duty in a deadly warzone, decides to have a few drinks and a bit of fun in his hotel room with a woman he's just met, how on earth is that anyone's business but his?
I can not speak with any authority on whether or not Prince Harry should be discharged. I would be greatly surprised if that happened.
However, I will make a few comments. First, if one invites a group of strangers into their home, cavorts with said strangers, allows themselves to be photographed and then allows his guests to leave, then what happened is no longer "private." Said person invited the general public into his home and allowed them to photograph the occasion. Now, the pictures belong to those he invited.
As to your last comment, "How on earth is it anyone's business but his?" Well....That would be because he allowed the group (more than a couple) of, as you call them, "totally unscrupulous money-grabbing women" to take pictures of the evening and one of them decided to make them public.
I also find it very interesting that Prince Harry is just a poor, victimized, good natured, soldier boy out to blow off steam by getting drunk and naked with women he knows nothing about, but the women are "unscrupulous", "disgusting," and "money grubbing." It seems to me that the lack of scruples and disgusting behavior goes both ways. He treated them like objects and they treated him the same. Were they supposed to be so honored that he used them for the evening that they would just revere their pictures forever??? Prince Harry is reaping what he has sown.
I guess those women figured if they were allowed to take the pictures on their phones and leave with them, they could do what they wanted with the pictures. They belonged to them after all.