It starts out as an intriguing concept. There are obvious security implications, though, and they seemed to have addressed them here. Unfortunately, that page makes the following mistake:
Only the Zero Install software itself is a potential risk to system security. With traditional (non-zero-install) systems, every application, library and documentation package is a potential root compromise.
Of course, this system is all about downloading software off the Internet and running it on your local machine, every piece of which is a potential risk to system security. Thus, this particular “fact” is snake oil, and these people now have a very high burden of proof to overcome before I consider their system trustworthy.
It’s tempting for people to think they’ve solved a particular security problem just because they handle it better than other people. There may be benefits to the Zero Install approach, and they may even be a theoretical improvement over other systems. But “almost right” doesn’t cut it in security, and if they’re amateur enough to make claims like the above, why should I believe that their execution will be any more competent?