As I understand it, the moderator rights and duties proposed here are not intended to give special rights to moderators, but to ensure that moderators are protected against mistreatment in the same way as normal users, encourage that meta investigations of moderator actions are carried out in an appropriate professional way and tone as can be expected on a high-level professional physics site, and that in case moderators do something wrong any punitive measures meet the severity of the wrongdoing as can be expected in any democratic community with a reasonable and fair legal system.
In my opinion, it is of paramount importance to settle these things and come to a consensus, to avoid killing all incentive for serious professional physicists to be nominated in the upcoming moderator elections and to help us with moderation on PO any time in the future.
Let me adress and explain separately how I understand the different parts of the proposed moderator rights and duties.
Moderators donate extra time for tedious activities needed for the proper functioning of PO, and should be valued for this. The guidelines should be such as not kill all incentives for professional physicists to help us with moderation in the future. In particular, moderators must be protected against abuse or unfair treatment in the same way normal users are protected. Moderators have all user rights, including that of being treated with respect, the privacy of their private messages, and that of being allowed to have an anonymous identity.
This paragraph does not propose to establish additional rights for moderators, but just says that moderators are users (and human beings) too and should therefore be treated as such in the same way as any other user (or human being) on PO. Even though this seems to be a no-brainer to me and even if we hope that no corresponding issues will come up in the future (again), to me it seems to be a good idea to publicly state somewhere what this paragraph says.
The penalties for moderator misbehavior should be considerate - not only a choice between forcing to resign vs. simply accepting an excuse.For example, penalties could consist in temporary suspension of moderation for increasingly long periods (1 week for first serious offence, 1 month for the next, then forced resignation for the next). This should happen only for _continued_ grossly bad activities that harm the scientific goals of the site or the user rights.
In any constitutional democracy, the punishments of violations of the law correspond to the severity of the violation. There are appropriate nuances for punshiments that can be issued, ranging from monetary fines, to prison sentences of various lenghts, up to the death sentence in some countries. PO envisages until now only the possibility of accepting an excuse (which corresponds in the real-world analogy to a small monetary) fine and the immediate dismissal of a moderator (which corresponds in the real-world analogy to the death sentence), so I agree with establishing some graduation of punitive measures against moderators as proposed here.
Moderator penalties should be imposed only according to clear and fair rules (and I am fairly open about how these would look like). Ordinary users should bring up apparent offences against moderators in meta in a polite, constructive way, but they cannot enforce a moderator penalty.
The most important sentence in this paragraph is in my opinion the first one: Moderator penalties should be imposed only according to clear and fair rules.
The second sentence is the proof that the proposal for moderator rights and duties does by no means want to prevent questioning and investigating moderator action on meta. On the contratry, bringing up controversial, bad, or wrong moderator decisions and actions on meta is encouraged! But it should be done in a professional tone and way, as it can be expected on a high-level professional physics site. This seems important to me, and part of it is probably already adressed by the new editing guidelines.
For the reasons explained above, I therefore support establishing some kind of moderator rights and duties in the spirit of this proposal (the exact way this gets done seems less important to me).