I used it professionally from 2012 - 2014, and I know of about a half a dozen companies either developing things in it or supporting it as part of saas offerings. Not that many, but each group that I know of made the switch after extensive reviews of other language options, and they've all had positive experiences so far.
Yes, I've used it for a number of academic research problems in biophysics. Our first manuscript that used it is in review right now.
To get "real work" done, I stuck with the 0.3 line. I've found it to be quite stable. Master is quite lively but should be settling down soon, at which point I'll migrate.
Not sure they are on HN, but I know a few companies at least are using the JuliaOpt[1]/ JuMP[2] stack.