There could be the "Hit rating is your friend" tutorial explaining that if you can't hit the boss, you can't DPS. There is also the "Stay out of the boss's cleave" for those people that want to stand next to the tank during Onyxia. Speaking of Onyxia, we could also just do a general "Dragons: Where not to stand" tutorial telling people to avoid the front and back. There is also one that most new healers run into "A dead healer can't heal the tank" explaining that you also need to keep track of your own health as AoE damage can kill the healer.
While some of those were meant to be sarcastic, other ones we tend to take for granted. Some new level 80 characters have never experienced the game mechanics we often feel should be general knowledge. So, I take the question to you: What new tutorials do you think should be added into the game?