None of the points mentioned are meant to be an attack on anyone - thy are merely ideas worth considering in probably many communities, not just ours.
This can be viewed as a continuation from the "On /r/Bitcoin moderation - three years in review" blog post.
Head moderator responsibilities
Everyone has different approaches to moderation. Personally, I find myself starting with a lot of enthusiasm early on and later petering out over time as more people join the team and are able to take on the responsibilities. Being the second moderator on /r/Bitcoin for a long awhile and facing the community backlash at our top moderator gave me an opportunity to think about how I would run things. While this might not be an ideal solution for everyone, here is the approach I might take - focus on being the moderator of moderators and an arbitrator between them, rather than dictating the direction of the subreddit.
My personal approach is that everyone makes mistakes - moderators are no different and I'm no different. The best approach to take is to fill the moderator positions with people that aim to support the community and see it grow. Most importantly, however, those people should be open to discussing and challenging views held by themselves and other moderators as needed. One person might make a mistake, but if five people agree on something, it is less likely to be a mistake. If someone disagrees, it is important that they express their reasoning and let their peers come to a conclusion whether something needs to change or not. Many of the /r/Bitcoin moderators, both past and present luckily are able and do voice their opinions even if it's not in line with the current rules.
Being the top moderator on Reddit gives one the power to control everything in the given community, but in my opinion that power should be used very rarely. Ideally, the top moderator of the subreddit would perhaps only step in if the other moderators are acting against the community and need to be removed. This could mitigate the use of moderation to push one's agenda - if the top moderator doesn't actively moderate, they can't change much to suit their agenda. Other moderators know that if they usurp the community, they will be removed. Thus some balance of power could be reached for the betterment of the community, provided the top moderator could be trusted.
At times the moderators might need to discuss some matter anonymously. Perhaps it would be an issue of removing a certain mod or other controversial topic. Unfortunately, Reddit doesn't leave many options for anonymizing one's conversations while still being certain you're talking with the same group of people. However, here is a simple solution to this problem:
Every moderator would create a random account. They would message someone saying they are a mod, but not reveal their original identity. That person would gather the list of all accounts that messaged them and present the list to the moderation group. Everyone would then acknowledge that the account they created is indeed on that list (without disclosing which account it is). If everyone acknowledges their account being present and the numbers match, you have a list of anonymous account that can be used to discuss anything without worrying about negative repercussions to your other account.
Having the anonymous discussions, it becomes much easier to discuss the removal of fellow moderators in an objective manner. You might want to call someone out on some actions they have taken or their general behaviour and see how other mods feel about the situation without becoming "that guy".
One of the responsibilities for the head mod would be to make sure the proper mods are removed (in case say, they are the second most senior mod that nobody else can remove). But perhaps the biggest mark of greatness for the top mod would be recognising if the community and other mods would not want them to continue at their position and step down like a true Roman Dictator, having put the power in the hands of the next worthy person chosen by the community and the moderators.
Another topic I've heard mentioned a few times comes in the form of insight into moderation logs. While those could probably be disclosed fully, they rarely tell the whole story - a good deal of moderation happens over modmail, which sometimes needs to remain private. It might be good practice to perhaps appoint a few representatives of the community to oversee the moderation process without being full moderators themselves. They would have insight into modmail and moderation logs, but shouldn't be acting as a full moderator. This could reassure some people that the mods aren't conspiring against someone or some company in particular, and it would also provide a good pool of candidates to pick from in case the moderation pool needs to be expanded.
Talking with the community
Communication with the community is important. Whether it's announcing policy changes or just having a general talk once a month, it might be useful to reach out to the community and hear what they have to say. This could boost the community's confidence in the moderators, help address some issues early on and hopefully make the relationships between mods and redditors better than what it sometimes becomes.
Those are some of my thoughts on how moderation in Reddit as a whole could be improved, or at least how I would try to improve it given the chance.