Quote Originally Posted by DDT View Post
(Actually you probably should say всем there anyway)
Здравствуйте + всем is less common than все, and some people can find it ungrammatical too. This is because здравствуйте, in its original meaning, is a verb in imperative. So все is an обращение (not sure how to say it in English) and requires nominative. "Здравствуйте, все!" is similar to "Извините, молодой человек!", "Подай мне карандаш, Ира!" and so on.

On the other hand, привет should be used with всем, not все. "Всем привет!" This expression can be considered as a shortened form of "Я всем говорю (посылаю etc) привет", so dative sounds good here.