King Charles wearing his dress uniform and white gloves... doesn't he have people to clean his stuff for him? I'd be embarrassed of those gloves as a private, let alone as the king.
Not sure if it's the same in all branches but Army regs specifically say that you have to hold the salute until it's returned, or for six paces after passing the person/thing you're saluting. Saluting things is also not unheard of, for example when you pass the American flag.