Julia 0.3 is a solid release and many Julia users have been using the master Github version for the past few months for production use, academic work, and just messing around quite happily. There are relatively few breaking changes from 0.2 to 0.3, with much better package support - so upgrade as soon as you can.
Julia 0.4 is likely to be a more "unstable" release in the tick-tock style that Linux used to have. Already been some great new things merged in, many more to come. I'd recommend not using the master branch of Julia at this time, and instead stay on release-0.3 if you like to build from source.