I haven't listened through the entire podcast yet, and only skimmed the transcript, so this might have been answered already. I know I already created several other questions and answers on this topic in various meta sites across the network, but I'm going to keep bringing this up when it's relevant regardless of how unpopular this opinion is.
You're talking a lot about the concept of community-based moderation, where users with large amounts of rep are involved in the moderation process. At certain levels of reputation, users gain a privilege related to moderation, like certain review queues, more flags to hand out, more power when reviewing stuff.
Problem is not everyone likes to have this extra privilege. Some people, like me, actively stay away from anything that remotely resembles a role of leadership or power because we do not AT ALL feel comfortable in such a role. We are natural born followers and supporters, but do not at all know what to do with or how to handle anything that gives us even the smallest amount of control over other people or content on a site. And being forced, or Shanghaied as I like to call it, into a role like this actually makes us uncomfortable using the site.
Note that I'm talking about more intensive moderation related to actual spam and offensive content. I don't mind closing things as duplicates, editing questions and answers for better content quality or throwing in the occasional reminder about accepting answers and editing additional information into questions, because this isn't moderation, but editing. Editing is about improving the quality of individual pieces of content. Moderation is about improving the overall quality of the site through removal of content that isn't suitable.
For the overall site this is mostly fine. since the top bar redesign there is no longer an obnoxious indicator near the moderator queue button for outstanding moderation items. This has removed a large amount of the stress since it's now easier to ignore the moderation queue entirely.
However, there is still such an indicator on the chat footer: the blue orb that indicates flagged messages. There are some fundamental issues with showing chat flags to everyone with enough rep. The first is that chat has a greater variety and flexibility of topics, meaning the things posted in chat sometimes tend to be slightly more outside the acceptable than the main site. The second is that there is a large variety of non-English sites with non-English chatrooms, but these messages are shown to users from all rooms, not just those with significant rep on the particular site. I have no rep for any of the Russian accounts, yet I still see flags for them and I have no idea what to do with them. Same with the dozen or so other sites that are foreign language. Finally, chat flag visibility is AFAIK based on rep across the network, so having a lot of smaller accounts easily brings you over the rep floor t see those flags.
I think at least one change that would make most of these problems less of an issue is to make it so you need at least some non-automated rep from a site before you see chat flags for that site.