What language(s) are sufficiently implemented on parrot for internal production use?

Lua reached feature parity with Lua 5.0 and it's close to 5.1, if I understand correctly. PIR is also stable.

Is there a list of what needs to be done in order for Parrot to safely support a single language?

That depends on the language's features.

Would it make sense for the Parrot effort to put some work into polishing those pieces right now?

That's what we're doing!

Personally, I think having software in a ready-to-ship state as soon as possible makes a lot of sense.

That's why we make monthly releases.