I'm a developer for the analysis code yt ( @yt_analysis ) which is a big user of BitBucket for code review and versioning. Our tool is mostly applied to astrophysical simulation data, but we're expanding to address other domains like nuclear engineering, oceanography, and so on.
We'd very much like to be able to deploy a mechanism to view this data in an external (or internal, although I am not familiar with the security implications of that) viewer very easily. Having the ability to design "apps" that display buttons or iframes for specific filetypes would be incredibly useful, and I think would make BitBucket much more attractive for development and deployment of particular classes of applications.
As it stands, we absolutely love the inline display and diffing of images, but being able to develop, deploy and select "apps" that we enable on a per-repository basis (or even per-account basis) to view specific filetypes would be amazing and really quite transformative for online collaboration around code, products, and data. Being able to deploy, say, "view in Sketchfab" or "view in [custom] D3" would be revolutionary, especially if individuals were able to develop apps the way that hooks can be developed. Being able to select "apps" the way "hooks" are selected could be pretty amazing for Bitbucket.