I run Movable Type blogs for a few people. Several of them have used popup comments in their templates, but it appears that at some point, there was a revision in Movable Type's source that made it impossible for the popup comment script to work. Now, when you pop-up their comment window, it shows an 'Invalid request' error. After looking at lib/MT/App/Comments.pm, it appears that this 'Invalid request' error is returned whenever the request is not a POST. Well, the comment popup template is initially a 'GET', so this error would seem to show up any time that you initially pop up a comment window.
So, is there now some other way to implement comment popup templates? Or are they no longer allowed?
We're running MTOS 4.12.
Reported on Movable Type 4.1x

They're certainly allowed, but not part of the templates anymore AFAIK. If you want to do implement them, what I would suggest is that you create a new entry template modeled on your individual entry template, but with most of it stripped out, save for the comments part. The whole with id "beta" should be able to be taken out of the default template set as well to achieve something close to parity with the original popup template look. Then, you'll have to call the popup JavaScript, and supply it the url of the second individual archive mapping.
That's the best suggestion I could think of off the top of my head.