What do you like best?
Back in college I used Zotero for everything. Its seamless Firefox integration and later integration with Word were exactly what I needed, and unlike EndNote, I could install it on all my own devices with no trouble and no fees. I now use it very occasionally to curate my personal reference library, and it's still got the magic, although I no longer use the advanced features.
What do you dislike?
While many, many custom styles were available, it was a HUGE pain to start from one of these and modify it slightly. This may have changed, since I rarely need to cite in a specific, obscure style these days -- it's worth a look.
Also, everyone else uses EndNote.
What business problems are you solving with the product? What benefits have you realized?
I am a freelance researcher as well as an editor and Zotero manages my references excellently. I only use it when I'll be the only one handling the reference section since it's so nonstandard, but it's lightweight and flexible and does a terrific job.