Nice article, though I think formality is not *that* important. I am fine with students who are informal in their emails. I advise students to avoid (1) excuses, (2) complaints, and (3) entitlement:

“My cousin got married, I got a flat tire, the tow truck got lost, and my life is just really very busy; and your posted notes don’t always match the lecture, the TA is not very clear, and the textbook is confusing; so it is vital that you send me a summary of lecture, meet with me one on one, and take all this into consideration for *my* final grade.”