I've watched people stick their feet in their mouth, bite down hard, and somehow not feel it. It's embarrassing to watch. In reading articles about Alex Rodriguez (A-Rod), what is striking is how he isolated himself from his teams.
1. You may have leftover baggage from your past misdeeds, whether of no import or of serious import. Do you know your reputation from your last position? Probably it is best to have the misdeeds out in the open, so no one can talk about them. If you've proved to be a disreputable person, or a systematic liar, now is the time to straighten up and fly right. If your dissertation is sprinkled with plagiarized passages, you may want to go into another profession and stop using "Dr."
2. Never take on students complaints about one of your colleagues. Send student to the colleague. (The exception is "mandatory reporting.") Or, to the dean.
3. If you have gotten your job by curious means, say a "greased" appointment process, or because you are friends with someone, or because to appoint X they had to appoint you too, you'll need to face up to that fact, perhaps by becoming a very effective performer. But those means are likely to undermine your authority, unless you turn out to be an academic star. In any case, the curious means are likely to undermine your "someone" unless, again, you turn out to be so wonderful. To be one of the dean's "boys" or "girls" is not a good position.
4. If you went to a more distinguished university than the one you are now working at, for your doctorate or post-doc--shut up. Lots of people are in that position. Don't compare. Make sure you don't wear lots of Yale or Harvard or Oxford hoodies. Don't brag. On the other hand, you can be loud and loyal about your undergraduate institution.
5. Do not spy on your colleagues, or allow your students to be your agents. Telling your colleagues what to do based on such spying, is a recipe for your being stigmatized. Never become the mouthpiece for unhappy students. There are deans and associate deans whose job is just this.
6. Deans can ask faculty not to do things, although a wise dean keeps their counsel and uses it quite sparingly. You are quite unlikely to influence a colleague to change their ways. Deans have to assume that whatever they tell someone will get out. People have to tell someone.
7. Be careful about your emails. Emails last forever.
8. Your authority is usually limited to your expertise in your field. No one can attack your authority if they differ with you on other matters, since you have no authority on those matters. If you have bureaucratic authority, keep in mind that that authority is fleeting and goes with the role not with you.
9. You surely want to be available to mentor and counsel your colleagues, but be aware that what you may consider your exemplary performance may not be so judged by others.
10. Never refer to your students by adjectives such as brilliant or deep, or refer to your department as top-ranked or whatever--unless you have the kind of evidence that would be probative to your skeptical colleagues. If you are president of the institution or a dean, you a more like the used car salesman, and you can say what you like.
11. There are some faculty members who do not publish, but who are widely admired by their colleagues. But for most of us, if we do not have active research and publishing careers, if we do not regularly receive competitive grants and fellowships, we do not have much authority at all. Having a doctorate does not convey much, and you should not allow people to call you Dr. At some point in a career the accumulated achievements buy you lots of leeway, but unlikely before you are in your 50s if you have begun your career by age 30 or so. If you are a superb (or not so superb) teacher and publish about teaching, that's fine. In general, once you enter administration, your authority is bureaucratic, and your research authority is not to the point. There are some wonderful exceptions to this.
12. Your notions about standards and quality, if they are in accord with the strongest in your field, are likely to be reliable. Students who tell you that what you consider plagiarism is just what they were taught are in need of re-education. Students who implicitly threaten you with allegations of whatever sort, if those allegations are manifestly false, should be encouraged to see the dean immediately. If students write you email that is insulting or nonsense, do not reply to the email, and if asked about it, indicate that you deleted it without really reading it. In general, do not reply to any email that is accusatory or nonsense. Save it in a folder. Don't try to correct misunderstandings. Just ignore. You cannot afford to get drawn into others' idiocy.