Making Hard Decisions to resolve larger disputes involving multiple people – this is usually a mistake because large disputes are often really hard to understand (so you usually end up picking a side, with that being the wrong side), and they normally fall into one of a handful of archetypes: it's better to analyse them from the archetypal perspective, then take action based on that.
Believing that those who behave in Certain Ways have good intentions. (I've fallen afoul of this, too.) There are certain behaviours that, despite appearing benign or even benevolent (especially when considered together with the actor's explanations), have ime a 100% "actually that was malicious" rate. These are quite sophisticated bad actors, and I'd rather they don't know the tells I've identified, but one of the tells involves the charismatic weaponisation of "cancel culture" by abusers, with part of the tell being to wield "the people's" authority (for some value of "the people") to attempt to modify the composition of a moderation team. (I haven't seen the complete tell in this situation, so there are still benign explanations: this just explains my bias in https://news.ycombinator.com/item?id=45403417.)
An impedance mismatch between the behaviour of the new moderator, and the behaviour expected by the community. For example: erring too heavy-handed, or too hands-off; mistaking banter for abuse, or abuse for banter.
Not speaking truth to power. In most BDFL-type collaborative projects, the founder guy turns out to be really ill-suited for the role, in one important respect. (Examples: Richard Stallman, Linus Torvalds, Andreas Kling.) In many cases, an intervention can resolve this, and save the organisation for a time (e.g. the 2018 Kernel Maintainer's Summit: https://lwn.net/Articles/769117/); in other cases, the organisation heads down the road to irrelevance (e.g. the FSF). (This is of course not the only kind of situation where you'd want to speak truth to power.)
Speaking truth to power undiplomatically. Power is still power: if you suspect the guy in charge is going to take your intervention badly, raise your concerns to the court jester. If you suspect the guy in charge is a bad actor, tread carefully.
Attempting to use an ethical philosophy not conductive to moderation. These include "let's let everyone do everything not illegal!", "if you have anything good to say about bad people, you're a bad person!", "those who disagree with me are bad actors", "can't we all just get along?", "I want to make sure I'm temp-banning the right person before taking action", "it doesn't matter if I'm temp-banning the right person", "people should follow the rules", "people can ignore the rules if they have a good reason", "we don't need lots of rules", "we should design rules that work for every situation", and "we should rely on moderator judgement".
I think that question would take a book to answer, and I'm not aware of anyone having written that book yet. (I'm certainly not the right person to write it.) It's not that hard to work this stuff out for yourself, but…
Trust not your self; but your Defects to know,
Make use of ev'ry Friend——and ev'ry Foe.
A little Learning is a dang'rous Thing;
Drink deep, or taste not the Pierian Spring:
There shallow Draughts intoxicate the Brain,
And drinking largely sobers us again.
You can completely destroy a community if you've found some of the fundamental principles, but not those which counterbalance them. (And you don't even need a formal position of power to accomplish this.) It's this partial understanding that I was referring to, in that last paragraph. In the absence of a good book, I don't think a moderator can learn these things without good mentors, a rogues gallery, and many mistakes – but those mistakes can prove fatal without good mentors to fall back on.
Could you elaborate?