(Don't you hate it when a word is on the tip of your tongue and you can't retrieve it?) What adjective describes a person who is always policing others; zealously judgmental? Maybe I'm looking for a noun. Is there a psychological personality type that fits this description?
Pharisaical is good term. It means marked by hypocritical censorious self-righteousness according to https://www.merriam-webster.com/dictionary/. For those who are familiar with the New Testament, they will understand well how this attitude was exemplified in the Pharisees of Jesus' day and how Jesus reproved them for it.
It looks like the word you're seeking might be officious.
assertive of authority in an annoyingly domineering way, especially with regard to petty or trivial matters.
2: volunteering one's services where they are neither asked nor needed : meddlesome. Officious people who are always ready to offer unasked advice
I remembered the word I was trying so hard to retrieve, and I actually didn't articulate its definition accurately, but this is what I was seeking: hypervigilant.
It turns out that hypervigilant isn't the same as Pharisaical, which comes closest to what I was trying to convey.