I wanted to go back to a comment made a few posts ago, about how there can be the fired employee's side of the story, and then the company's side which they aren't allowed to publicly broadcast--in my thread about handling church firings, this is the exact issue that's come up. And it has nothing to do with social media, but everything to do with human nature and people in a small community spreading rumors that fit their own agenda.
Social media is really just amplifying the ways humans have always talked and spread information--both useful things and harmful things. I've also heard about teachers being careful about their behavior that could be witnessed by the public, even on their own property, for fear that "having one beer at home" would get amplified back to their employers as "drunk in public." It's not that an A+ teacher would be immediately fired because one person made one minor, uninvestigated complaint about them. But it could be the straw that breaks the camel's back. Maybe the teacher is really just coasting along, doing a lot of other minorly bad things. Or, maybe the teacher is decent but just doesn't "fit in" with the others--could be something outright discriminatory, or could be that the teacher challenges the status quo. Coming from a small town, you see a LOT of that--you know if you rock the boat at work, doing something worthwhile, you have to be extra-careful outside of work to not give your professional enemies any ammunition at all against you.
I'm not saying any of that is right, just that it exists, and people have to be aware of it as it relates to their jobs. It's always been true, well before social media.
Also, in my personal experience, it's incredibly hard to fire someone, at least someone on a salary. Between unions, corporate policy, the higher-ups not wanting bad publicity, and just plain inertia, you normally have to document that you have repeatedly talked to someone about their problematic behavior and given them opportunities to improve, often for months; and you have to really go to bat with your superiors to get someone fired. It takes work, and confrontation, and most people are already overworked and dislike confrontation enough that they'd rather tell everyone else to just deal with it than go through the trouble of firing someone. Obviously that's not true in 100% of cases; and there are certainly people who are willing to do the work to unfairly fire those they simply dislike. But in my career I've been much more troubled by people who need to go and yet stick around, causing more work for others; than by the idea that someone might be fired unfairly, over a minor rumor. And it might be cold comfort, but honestly, if an employer is going to fire you unfairly over a minor rumor, you are better off not working there, because they will almost certainly do other bad, unfair things.