Edit: A follow up question has been made by KorvinStormast here.
This has the potential to be a flame war, so I encourage everyone who involves themselves in this to self-moderate. On the other hand, since this is focusing on doubts about our moderators, I'm also asking that nothing gets deleted without a comment saying that it should be deleted either coming from the same side of the debate, or from someone who has been agreed upon as neutral. (At least until we agree on something better.)
I've noticed that not everyone trusts our moderator team anymore, and I don't know all the reasoning behind this. Earlier today, I asked on Meta.se about what appears to be a schism in our community over our moderators. I didn't bring up too many details, as I hope that we can resolve this by ourselves. If you have not noticed any issues, that's fine.
I am proposing three questions.
One question asking who everyone can agree on as neutral. (This one.) This person will not be allowed to propose any arguments. If both those who do not fully trust the mods and the mods cannot agree, we'll have to put our big boy pants on, and keep going without a mediator.
One question (not this one) asking what went wrong, and how we got here. Answers would be whatever complaints either party has about the other, with the comments on each addressing these concerns. If we can reach an agreement in the comments, the answer gets edited.
The last question (also not this one) would address where we are going from here, and how we plan on avoiding this situation in the future.
That's the best, most fair and impartial way I can come up with. Does anyone have a better idea?