So... I just installed Ubuntu 14.10 on my (new) home PC, and chose BTRFS because I figured it was stable by now. Should I be worried? I do plan on playing with docker.
When it goes wrong (about every 4 months for me), you will end up in a nightmare. Generally attempts to fix issues will make things worse, various tools and pages contradict each other, and the devs are only interested in the latest kernel version. Much of this is deliberate - the code is written to not sweep things under the rug, which means you can hit problems and not recover. Use backups and make sure you can restore.
The reason why I keep using it is because there is no silent corruption as you get with ext4. A scrub can verify every byte of data is unaltered and recover if using anything other than single profile. Compression, volume management, cheap snapshots etc also make working with it nice. Until things go wrong.
The single biggest "going wrong" is running out of space. Copy on write filesystems by their nature leave existing content alone and write new information in the spare space, eventually doing a garbage collect of obsolete data. When you are out of space that gets rather difficult with bizarre symptoms and tricky recovery.
You can use tools like LVM and md as a layer underneath ext4 to provide some resiliency, but there is a learning curve and two sets of tools to work with. Changing around disk/partition sizes isn't much fun with them.
It's too bad, I really love the idea of btrfs, but there's no way I would ever run a filesystem on it yet.