Hackers "dinopio" and "Edgan" have managed to gain complete filesystem access in 1.1.1. This is NOT full write access, and jailbreak is NOT achieved yet. This was managed by using symbolic links before upgrading.
Our friend Erica Sadun over at TUAW has put up a blog about her experience recreating their method here. We're getting close, folks!
p.s. No, Mobile Music Store does NOT work on 1.0.2 yet. Erica surmises it may be missing 1.1.1 frameworks, or simply an activation cert like YouTube needs.