The project has 2,100 open issues and 8,500 closed issues.
The stability more or less comes down to the community moving away from targeting nightly, and that can only happen when all of the fires are put out. There are still a lot of breaking changes and clean-up being done in the final hour.
Some people consider stable to mean that the language is "production ready", which often implies a complete set of common libraries. There is still a lot of work to be done in this regard after 1.0. Doing the nightly build whack-a-mole is too frustrating for many, though, so 1.0 will help a lot for developing the ecosystem that a "public ready" language needs.
https://github.com/rust-lang/rfcs#active-rfc-list
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discussion re: stdlib and 1.0 https://www.reddit.com/r/rust/comments/2mo0zb/the_race_towar...