In a project I'm working on [1], I'm planning to provide a browser extension that verifies the source code is digitally signed and that it matches the source code published on GitHub. I believe this creates a pretty good security model for a web-based app, even more so than most desktop programs. Some more information from the security page [2]: The browser extension provides improved security by verifying the integr…
So what happens when github goes down? I'd argue a better source for this sort of thing would be to put the hash in dns, either directly in a txt record, or using hacks involving A or AAAA records. Your nameserver almost certainly has more security than your github repo.
Alas, client-side JavaScript doesn't speak DNS. You'd have to go through a server, which would mean you'd lose anything you might gain.