I'm bothered that this runs periodically. Will it auto-update code? How secure is the auto-update process? Who can run an auto-update? Does it run as root? If so, why?
If it was a one-time manual run, that wouldn't be so bad. You can snapshot a system, run it, and see what it changed. When it gets to run on its own, that's harder to test.
It's not like "take this binary blob from us and run it as root on your machine", it's like "we have an open source project that would like to work with your upstream OS distributor on exactly the same terms as, and in exactly the same way as, the other tools that you're using on your server".
Edit: If you want to follow along with, audit, contribute to, help package, etc., our preview client, it is available at
https://github.com/letsencrypt/lets-encrypt-preview
We will also welcome people to create their own interoperable software, so if you don't want to run our client or any of its dependencies, or if it doesn't work well with your serving environment, you can create your own alternative. (Hosting providers or CDNs that want certs for sites they host, for example, could create their own tools to deploy them, instead of using our tools.)