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A plea to the people behind Fermat's Library - please port the Librarian extension to Firefox, too! It has full support for the WebExtensions API that Chrome uses, so porting is usually just a matter of a small tweak to the manifest.json and re-uploading it to the Mozilla Add-on Gallery.
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Unfortunately, it seems like these comments are only visible to Librarian's users, which doesn't make it much different from Hypothes.is [1] other than being limited to arXiv, and makes comments less discoverable. arXiv should really add such a feature itself/have open sourced its code so they could've added it there.

[1] http://hypothes.is/

It's tricky. Many (most?) researchers would rather have a closed discussion with other researchers with domain expertise than an open one where they have to deal with public comments.
I've always thought stack overflow could be the start of a model for an academic archive.
I think this is certainly true. Research papers are typically written so that a person with training in the field can understand and replicate the work. Note that the general population is not the intended audience. Mediums like news articles and blog posts are a more effective way of explaining the background and significance of a certain piece of research to the masses.
Yes, but that's still hard if half of those other researchers are on Librarian, and half of them are on Hypothes.is.
I will toot the hypothes.is [0] horn again. It is possible (if sometimes finicky) to use it to annotate pdfs. See for example a demo annotation [1]. The other really cool thing about this is that hypothes.is fingerprints pdfs and uses a URN to uniquely identify them, so you can annotate a local copy of a pdf (in the browser) and those annotations will show up on any other copy of that pdf anywhere on the internet.

0. https://hypothes.is/ 1. https://hyp.is/hZbgFO_ZEeemmt9kojvZIA/arxiv.org/pdf/1712.100...

There have been many comment layering systems for arxiv, none of which seem to have taken off. Also, users are pretty split on whether they want this: http://www.nature.com/news/arxiv-preprint-server-plans-multi... . Personally I'm not in favour of such a system, as it's unlikely anyone would spend enough time to write a high quality comment that won't detract from a paper.
I would love to see the addition of peer reviewed comments. Curation is key, of course.