It would be cool if it was possible to submit pull requests from Bitbucket to other big DVCS hosting sites. This would of course require collaboration with them.
I'm thinking of a system where GitHub can send a request to a URL at Bitbucket with information about the GitHub repository and branch to pull. Bitbucket would then present this like a normal pull request (maybe even do the pull into a temporary repository so that you can show the diff) and if the user approves the request, the pull is done.
Comments on the pull request should probably be directed back to the original site.
This was discussed here first: https://plus.google.com/108957994038017966408/posts/PaB9jVuEkwt