The basic idea is to embellish make the list of literature cited in an article with information that might help a reader decide whether a given citation is worth reading. One clue might be how many people on Mendeley are reading that article. So, my app takes an article, extracts the list of cited literature, and for each article with a PubMed identifier it asks Mendeley "how many readers does this article have?" For now the app is restricted to using articles from the BiomedCentral series as these have Open Access XML with literature cited lists that contain PubMed numbers (PLoS articles, for instance, don't have these, for now I'm avoiding the overhead of finding identifiers for the articles). I'm using PubMed identifiers as the Document Details method in the Mendeley API doesn't handle DOIs at present.
The app is at http://iphylo.org/~rpage/mendeley/, and the default article I've chosen to demonstrate the app is Robust physical methods that enrich genomic regions identical by descent for linkage studies: confirmation of a locus for osteogenesis imperfecta doi:10.1186/1471-2156-10-16, but you can enter the DOI of any BMC article to give it a try. Below is a screenshot of part of the list of literature cited by this paper, together with readership numbers:
The default article has 4 readers in Mendeley. The readership of the articles it cites varies, but one article stands out with 208 readers.
There are huge limitations with this app (it doesn't cache the Mendeley results, so repeated use will exceed the rate limits), it is limited to citations in PubMed (could add support for DOIs and title searches), and only BMC articles can be processed.
What would be interesting is to extend this in other directions. For example, if the user had a Mendeley account, it would be nice to flag which articles the reader already had in their library (and perhaps have the ability to add those that weren't to the library). To personalise the citation readership display I'd need to add support for OAuth, which Mendeley uses to authorise access to user accounts.
If Mendeley were to provide more social features in their API then we could add flags indicating whether any of user's contacts have any of these articles in their libraries (your decision to read a paper might be influenced by whether a contact of yours has read it -- think of it as a resembling the Facebook "Like" button). Or we could display the readers themselves, so you could discover people with potentially similar interests to your own.
My twitter stream has been full of complaints about the Mendeley API — life on the bleeding edge is not always fun. But the API does have the potential to support some cool applications, once it gets the kinks ironed out.