As a long Zotero user, I am continually excited about Paperpile and how it's destined to evolve with new features.
One thing which I would find indispensable is the ability to easily clip the entirety of the web page in addition to (and often in lieu of) downloading the PDF. More often than not, it's the text that I need, not the pictures. The ability to take that text and format it in different ways on different devices is liberating. It's ironic that as we try to get more digital, we keep locked into old ways of absorbing information. The ability to search through and annotate this data would also be fairly straightforward.
I would like the ability to clip the HTML of an article from the website and automatically add it to the citation. The pages that I currently have in my library were imported from my old Zotero repository. Currently I have to manually save a page and then manually associate it with a citation. The ability to simply clip the page would be great. The saved page could link to the website's CSS, be completely style-free, or re-formatted in an Instapaper/HTML5 type approach.
PubMed Central is a large proponent of this approach as well as many of the the larger publishers. Incidentally, the CSS and JS code used to create a PubReader presentation is available at their GitHub repository NCBITools/PubReader. Anyone can use or adapt it to display journal articles or other content that is structured as an HTML5 document.
(I thought this particular link appropriate as an example - http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3830982/?report=reader)
If this isn't on your horizon, I'd appreciate to hear other peoples opinions/workflows towards this goal.