Tom Stellard of AMD has spent the past few days working on getting the Radeon Gallium3D OpenCL stack in a state where it works to run the "bfgminer" Bitcoin mining application running on the open-source Radeon HD driver. After a few days, he has it working with some new code, but the performance isn't all that great.
Carrying out Bitcoin mining for now on the open-source GPU driver requires using Tom's own (non-stock) branches of Mesa, LLVM, and the libclc OpenCL library. There's also a patch needed against the bfgminer software itself. When using the code and patches, the application should work for Radeon HD 5000 "Evergreen" and Radeon HD 6000 "Northern Islands" (but pre-HD6900 Cayman) graphics cards.
When it's all setup, Tom writes, "the compiled kernel code for bfgminer is not very well optimized yet and there are still a lot of things that can be done to improve performance." So for now anyone serious about Bitcoin mining is still much better off using the proprietary NVIDIA and AMD graphics drivers with their much better GPGPU implementations.
Those interested in the Bitcoin Radeon Gallium3D mining details can find the information on Tom Stellard's blog.