Be prepared to see people who are normally reasonable become unreasonable about things that aren't entirely clear.
There is always a faculty member at every college that has the faculty handbook memorized. Make good friends with him. (Sorry it is usually a him.) He usually delights in being able to site bylaw and page number. If someone comes to you with a problem that ought to have a policy, use your fac-handbook guru. This person also usually knows Roberts' Rules; if you have to run those sorts of meetings, use and praise him/her for the knowledge held. His knowledge will become a thorn in your side unless you use him frequently and defer to him often. 99.9%, when it comes to college policy, he's right.
When someone is driving you crazy about a particular issue, suggest a meeting. If it really is a problem, the person will jump at the suggestion. If it isn't a problem, they'll back out of your office very fast and say that they think they can find a solution.
Always distinguish between "trouble-talk" and "problem-solving." If the person is just doing trouble-talk, they don't want you to fix things so don't try to. In that case, a pad with a furrowed brow are your best tools. How can you tell the difference? See point made, above.
I've said this on other threads, but when someone mentions a lawyer, pull out your "general counsel" script: Oh, you don't need a Dean, you need our general counsel. I'm here to help you problem solve, but if you want to talk about your legal options, you'll want to call this number.
Put everything that matters in writing. After you've talked with someone and you think that you've reached a solution, write a cheerful, upbeat note to them saying: "Thanks for meeting with me. I'm glad I better understand the issues. I think what we've decided to do is x, y, z. I can't start x until you get me a, b, c. So I'll wait anxiously for that information." This prevents the month later, angry call that says why didn't you do x, y, z. You pull up the email and say "Why, I thought I needed a, b, c, for you. Let me resend this email I have. Till then --I'll anxiously await that information!"
When an issue on campus becomes contentious, be prepared to be asked what you think. Or what the president thinks. Or what the Provost thinks. Be aware that whatever you say (and even if you don't say anything) will be spread with some odd twists to the original statement.
Be prepared to approach email in a wholly new way. It is a place where people go to vent. Never open your email unless you're ready for their vent. Never respond to vents until 24 hours have passed. The issue will always look completely different 24 hours from now.
Don't respond to email if your eyelids are hot. This is a sign that your blood pressure is up, and you will never sound rational.
Answer every email, even the most nasty, with a "Thanks XXX, That is really helpful information that I didn't initially know." It's amazing how that simple statement can change everything that you say after writing it. One of my high points in administration was when someone wrote an angry and hostile email about my department. I used that line: "Thanks XXX, That is really helpful information that I didn't initially know." I added, "I know you're a good friend to my department, the Center of Happiness of Hope,... Regarding the issue that you raise, it as actually more complicated than that..." Which, writing it now seems over the top, but we've been good buddies ever since.
No one can get mad at you if you invite them for lunch. If they were initially angry, the invite freaks them out and they never respond. If they actually want to solve the problem, they usually say yes, and the world is a brighter place after lunch.
That's probably enough for now, but I'll add more as they occur.