I like being able to keep my citations up-to-date as I am writing a paper without needing to spend a whole lot of time doing so. I appreciate that I can put my references into the library quickly from wherever I am accessing them from and also that there is a plug-in for Microsoft Word so that all the work I put into storing the citations is accessible.
Sometimes sharing references with others is a bit confusing. I am never sure if I can share a folder to a group, or if I need to create a group that has access to the references.
Also -- and this isn't Mendeley's fault, per se, but it's important to be aware of -- sometimes the automatic formatting of the citations isn't quite perfect (e.g., sometimes authors' last names get inputted in all capitals, etc.) so it's not quite a "set it and forget it" system.
In addition, sometimes the authors have multiple listings, for example; "Smith, J" and "Smith, J." are separate author listings, even though it is the same author. It would be nice if we could batch merge these more easily.