OK... so here's my take - in general, this guy and his attitude are your problem, until you manage to fix it, or make it someone else's problem. The ways of making it someone else's problem are pretty clearcut:
- help him and the company find a position that doesn't report to you
- eject him from the company
Things you can do with your management is ask for mentorship and guidance on appropriate actions. Either in fixing the problem, or removing the problem-maker from your scope of responsibility. I've done both in my career - generally, upper management should be more experienced, and have some words of wisdom, or at least be able to be a sounding board. But it's generally better to go with an approach of "I have this problem, my thought is to solve it this way... any feedback?" rather than "I have this mess and no earthly idea on what to do... please solve it for me."
So.. here's some (probably very long) guidance on both new manager head space things and behavior problem fixing.
Manager Head Space
When you move from a primarily individual contributor role (especially a technical one) and into a manager role - there's a big self-definition shift. Generally the best individual contributors are very, very good at technical contributions, and pretty good at team and other interpersonal communication. Managers are best when they are great at interpersonal communication - both inside and outside the team - and pretty good technically. See the switch? No one wants a manager who is a complete technical illiterate, but being totally clueless at human relationships is a much worse failing in a leader.
In this way, the choice is pretty clear - this guy isn't good at relationships, you are. I'd bet most the team is reminded that they dodged a bullet every time this guy opens his mouth - because who wants a manager that thinks belittling anyone publicly is an OK way to act?
When it comes to truly winning respect - the way you win is by being respectful yourself. You no longer have to be the epitome of technical competence - ask for opinions, ask questions, get people engaged in owning work, helping each other, and creating a positive environment for finding and fixing problems. That gets you the respect of the team. Maybe this guy will get a clue and realize he's the only one with a grudge. Maybe not. It's really his choice.
This does mean letting go of technical details. I found in my first role leading a team that I couldn't generally take on fun, new, challenging problems on an individual contributor level. I had to grow good judgement on a broader technical/personal level and learn how to see a big picture. Which meant, when I got hands on, it was intermittently and with caution. Taking on big chunks of work in an effort to keep my "rep" was a big fail, as I often had to drop this work to deal with managerial stuff.
Public Behavior Changing
In public, keep it positive. Don't call people out, it can be deeply humiliating and it's not a good way to get respect. Instead, focus on the work at hand. Realize that the bigger issue is that this guy is wasting time and energy on something that isn't the work at hand. If he would shut up and work on his work, he'd probably get a lot more done.
Things to notice, and deal with:
Ranting in meetings - if this stuff is coming up in a team meeting, get things back on track and focused on the agenda - presumably you had a goal in the meeting. Is the issue he's raising impeding the goal? Then work together to find a fix. Is it just blather? Then clearly and firmly point the team back to the actual goal - what needs to be done next to get there? If this happens repeatedly in the same meeting - do raise it clearly and firmly - "I understand your complaint, but we are focused on X agenda item. This is the Nth time you've gone off topic. Please focus on our agenda so we can finish the meeting... if you have issues or concerns about other topics, let's speak after the meeting". This is particularly powerful as EVERYONE wants to have a productive meeting and go on with their lives. No one likes sitting in a boring ranty meeting. You might even get some applause if this has been particularly onerous.
Ranting between meetings - Once you beat out interruptions in meetings, you'll likely see an increase in ranting between meetings. If this is a 1-5 minute rant that happens once a day, I'd say let it go... there's only so much that's worth your time to fix. But if you are hearing 10+ minutes of ranting (total) per day, interject. Come over to the guy and say to everyone - "hey, I've been hearing this conversation for a long time now. Are you solving a problem? If so, what's the actual issue and how do we fix it? If not, please go back to work." When the issue is stuff like "you have a typo in your email" - point back to the bigger picture - did it make the email impossible to understand? (if so, shame on you! fix your typos!) if not - is this guy so dumb that a single typo really threw him for a loop? I'm not sure I'd call an employee of mine "dumb" - but saying "did this make the email impossible to understand?" is pretty demeaning, and the context is clear - don't rant about really trivial stuff, it'll make you look stupid.
Private Behavior Changing
There's a big difference between what you can do publicly and what you can to privately. The morale of the team is a part of every public interaction you have with this guy. Showing that you will treat even an enormous Pain in The you-know-what with basic human decency raises your cred with the whole team. Focusing on everyone delivering valuable work sets the scene for a productive group. And a fight takes two people.
In private, though, is a different story. Privately, you have the opportunity (and sometimes the obligation) to be brutally clear. How brutally clear you can be and the words you use are something that is well worth rehearsing with your upper management. As ever, demeaning words are a no go. But being very clear and very specific about behavior that needs to change is part of your job.
If you don't have regular 1 on 1s with your whole team, it's something worth considering. It's a tool many successful managers use and it helps avoid singling the problem creators out. And - even a really AWESOME employee may have issues, hopes and dreams they don't want to discuss in public. I find that with my good team members, 1 on 1s are actually invigorating for both of us - we talk about issues, we help each other, and (the really fun part) we plot and scheme new ideas and ways to improve - who doesn't love that??
With this guy - you really need a 1 on 1 on a regular basis. The first one is going to consist of:
- What do you want here at work? What's your career goal? What do you like about your job, what do you hate?
Could be, he'll tell you to you face that he thinks he should have gotten your job, and that he thinks you're a moron. In many ways that's best of all possible worlds. It's pretty clear to you that he didn't get your job because of the way he acts in public, and that's a great segue into the conversation - if this guy doesn't change his behavior, he'll never be a manager.
If not, you can still have some conversation about how you can help him work on his goal. One thing he might want to think about is - does he want to do the work to (vastly) improve his interpersonal skills so he can move into management?
- Next point: Feedback - you've got to give some sort of feedback.
Ranting and raving about anyone's mistake without taking it up with them privately is not OK team behavior. He needs to stop. Describe what you'd like to have happen when he encounters a problem (whether you created it or someone else did), and ask him behave that way. This isn't a point for discussion, it's a requirement for being part of your team.
Do all that, and you've done what I think of as "simple problem basics" - you've modeled the behavior you want to see - you've risen above issues, you've given negative feedback privately, you've focused the team on valuable work, you've treated people with respect.
An employee who is willing and able to be part of the team will be able to join the herd at this point and knock off the crap.
Escalation comes when that doesn't happen. Choosing to change behavior is entirely the employee's choice. We haven't developed mind control (that I know of...). Choosing whether you can retain this person in your team if the bad behavior continues is your choice. It's probably the worst choice you'll ever have to make. That doesn't make you weak, it makes you a caring human.
Escalation procedures vary from company to company, but generally if you've given feedback once or twice, clearly and directly, it's time to start escalating. This is a time when it is unwise to move forward without direct consultation with your management and HR. While the levels of feedback providing can vary, the ultimate end of the road is termination procedures, and those get sticky and legal quickly - somewhere along the way, someone will end up making clear to this guy that obeying the direction of his manager is a direct requirement for employment.
You and Your Management
Changing into a managerial role is a good time to also think about what relationship you want and need with your management and whether they can provide.
As a manager, taking ownership of problems - including personnel problems - is a big part of your job, and you can't really avoid it. But what you demand, in return, from your management is worth a discussion, or a least some commentary.
For example, I've found that once and a while, I need space to rant. I can't rant to employees - that's not cool. But just the chance to blow off steam, complain, whine and bang my head against the wall, is something I need from time to time. I will happily then pick up my problem and go forth and solve it. Not every manager is OK with that, so I actively cultivate that as part of my support network somewhere in the systems I work in.
Your management should as a bare minimum be prepared to trust your judgement, and also be ready to provide input when you have a strategy for something tricky. Be it technical or interpersonal - asking for a verification of your work when the stakes are high is a wise move. Management should be ready to give you feedback on what they care to have input on, and be ready to provide input when you ask. Be ready for the fact that sometimes "I don't care, do whatever you like" is valid input.