The story doesn't sound good...but I'm sure William was embarrassed enough when he realized his mistake. I do think that not thinking to check the badge looks like a sign of inexperience.
Sometimes I've wondered about how mature or experienced William is for his age. He doesn't really do royal duties, and I do understand that he has the military training to finish and all that, but recently I was reading about Crown Princess Victoria of Sweden. She's done some military training, but she's also attended Yale, completed several different programs of study, had work experience with the UN, learned several languages, traveled to many different countries and gained experience in international affairs and diplomacy...She's only a few years older than William, but she puts most members of the British Royal Family to shame.
Not everyone is academic or could accomplish what Victoria has, but I can't help wondering how useful William's years of military training are going to be. Maybe the royal family should have balanced out his training more...maybe a shorter stint in the military, and more public relations experience?
I would never write William or anyone off in their late twenties, and William is still young. But he's not that young--he'll be thirty in about 2 1/2 years--and he's probably going to be king someday. There is a difference between 18 and 28, for example. When people were saying Eugenie would never amount to anything because of the way she behaved on her gap year, I thought it was ridiculous; but I would probably have agreed more if she'd been ten years older. I think it's better to do as much learning as possible when one is young, so I hope William is gaining the experience he's going to need for his future role.