Everytime you load a webapp, you are trusting the server. Everytime.
In this case, the author is trying to take steps to make changes more visible, but at the same time they're making their own changes cause alerts as well. However, if the product stops serving such countermeasures for new users at some point, or plays a long con over say a year of really tiny, innocent changes that eventually break the system to check downloaded files, then we're no better than any other web app out there.
So unless you're inspecting and verifying the code you actually download yourself, even with these countermeasures, you're no better than any other webapp with the need to trust the code you download _every_ time.
Now, you're always trusting a lot of things like your hardware, your compiler, your package maintainer's compiler, your package maintainer, &c (http://www.win.tue.nl/~aeb/linux/hh/thompson/trust.html). The difference, however, is that I only need to verify that trust each time I update my code, which I can do when I choose to (baring any incompatible server changes) and after I perform any audit I choose to. (With a web app, there is often no (straighforward) way to audit the code _before_ it's been downloaded and executed.
I know I've been negative about all of this to OP. I'm sure he's done a tremendous amount of work. It just makes me angry when people claim they've solved one of the largest, most important problems in cryptography, when all they did is just ask me to trust them in a different way. It also makes me annoyed that for a security-focused product, there are very few details about architecture and cryptographic choices on the product's security page.
I don't mean to denigrate the work OP has done. I just feel that they're being foolish in their security-related claims.