I’m dissatisfied with what I consider to be shocking displays of arrogance by a certain moderator and would like to express my objections. What is the right way and place to do this?
There are many possible places, though on Stack Exchange this would be limited to Meta and Chat. Do remember that there is a Chat facility, which is where many comments are consigned. There are also innumerable social media outlets that are not specific to SE. The question of what is proper is a difficult one, because it assumes a particular function for a venue. Since main Law SE is about the law and not Law SE, that would not be a proper venue. The only guidance that I can find about Law Meta is this. The most applicable guidance there is that
Law Stack Exchange users to communicate with each other about Law Stack Exchange (asking questions about how the websites work, or about policies and community decisions)
Meta invites the community to discuss, debate and propose changes to the way the community itself behaves
which under a liberal construal means "complain about the conduct of others" (though a conservative construal would be that it's about the community and not individuals, thus questions about individuals would not be proper). There is a separate answer regarding moderators, addressed in the big Meta, which is about moderators abusing their privileges. If you believe that a moderator has abused moderator power, they have numerous suggestions. Note that they don't package this option as an open-ended venue for complaining, rather it is about objecting to specific improper actions (not wording like "regarding the action taken", "Flag for moderator attention"). The top of the food chain, a last resort, is "send a message to the Stack Exchange team via the 'Contact' link".
Your question was asked in Meta here ("Is there anywhere or anyone to complain to about the behaviour of moderators"), which was closed as a duplicate of the "abuse of power" question which, however, does not actually address the general question of moderator attitude. But, the two answers there did say "here on Meta". As you can see, there isn't agreement as to which Meta you should complain to. The closed question, which is the minority view and is aimed at moderator attitude, simply say "On SE Meta", but the holding of the majority opinion is more narrow, that abuse of power can be addressed on the specific site Meta.
Since you are familiar with how appellate procedure operates, you should realize that you can file a complaint on Ling Meta, then if the question is dismissed (closed or deleted), you can appeal to higher authorities (SE Meta or staff).