TypeError: e(".tooltip-demo").tooltip is not a function. (In 'e(".tooltip-demo").tooltip({selector:'[data-toggle="tooltip"]',container:"body"})', 'e(".tooltip-demo").tooltip' is undefined)
Not present in development...
Looks like we aren't importing all of the JS needed. Can you try rebuilding the docs on a clean checkout from git? Here is what the currently hosted docs have for scripts:

And this is my locally built one:

All the JS is in that docs.min.js bundle. For now I'm going to push a change to the docs to not use that version until I can figure out what's up with the concatenated and minified bundle.
Surprisingly enough everything works fine for me here: https://v4-alpha.getbootstrap.com/components/popovers/
I pushed up an update to use the non-minified JS right after my earlier comment. It works now, but I still need to look into why the minimized didn't.
I'm betting #21414 caused this.
Most helpful comment
All the JS is in that
docs.min.jsbundle. For now I'm going to push a change to the docs to not use that version until I can figure out what's up with the concatenated and minified bundle.