alt Hacker NewsImportant data should probably be worked on and stored with error-correcting codes, in addition to the hardware-provided ones. The Btrfs mention in TFA suggests that maintaining integrity of the Btrfs metadata is not considered part of the job description of Btrfs, but perhaps it should be.
BTRFS has checksums on all metadata. It isn't designed to cope with bad RAM but has been shown to be somewhat resistant to it to the degree that BTRFS developers can recognise symptoms in problem reports.
Whether a filesystem could be designed to operate in the face of random memory changes would be an interesting computer science research topic. But for getting working systems having RAM just not fail is a better option.