I accidentally sent my professor an email starting with "Dear professor"(without his name)?

Don't panic. Not even as irritating as misspelling one's name. If you don't draw attention to the omission, they probably overlook it whilst scanning the more relevant content.

I once accidentally replied to a professor rather than forward to a friend, with a silly personal message. Was chided for it, but over time these things deteriorate into little more than anecdotes.