How can I filter for items that have not been tagged?

Unfortunately, there's not a straightforward way of querying for content that doesn't have tags in the UI - only the opposite. However this could be accomplished with a bit of code to call the API to iterate through forum threads to build a list of threads without tags. Here's an example using server-side JavaScript which can be executed in the Script Sandbox of Widget Studio.

// which forum to loop through
var FORUM_ID = 4;

// get first 100 threads in forum
// this could be improved to iterate multiple pages of results
var threads = core_v2_forumThread.List({ 
    ForumId: FORUM_ID,
    PageIndex: 0,
    PageSize: 100
});

// filter the results to only those without tags
var threadsWithoutTags = threads.filter(function(thread){
	return (!thread.Tags || thread.Tags.length == 0);
});

// write the URLs of all matching threads
return threadsWithoutTags.map(function(thread) {
	return thread.Url;
});

Unfortunately, there's not a straightforward way of querying for content that doesn't have tags in the UI - only the opposite. However this could be accomplished with a bit of code to call the API to iterate through forum threads to build a list of threads without tags. Here's an example using server-side JavaScript which can be executed in the Script Sandbox of Widget Studio.

// which forum to loop through
var FORUM_ID = 4;

// get first 100 threads in forum
// this could be improved to iterate multiple pages of results
var threads = core_v2_forumThread.List({ 
    ForumId: FORUM_ID,
    PageIndex: 0,
    PageSize: 100
});

// filter the results to only those without tags
var threadsWithoutTags = threads.filter(function(thread){
	return (!thread.Tags || thread.Tags.length == 0);
});

// write the URLs of all matching threads
return threadsWithoutTags.map(function(thread) {
	return thread.Url;
});

Oh, you're on 10.x, so there is no server-side JavaScript. But the equivalent could be performed with Velocity.

Thanks! Very helpful. Could code like this be done in an Azure function? I'm not one of our developers but we've run these kinds of functions for other things before.

Not exactly, but Widget, Theme, Automation, and Embeddable studios in Community are a little similar to Azure functions in that it's custom code deployed and testable within the Community.

We're moving to version 12 in a month or two as soon as 12.1 comes out, so I may wait until then. Again, appreciate the help!