I'm sorry that you're having an issue while using Ubuntu One with No Script enabled.
The problem is not a bug in Ubuntu One. It's a configuration issue with the No Script plugin's ABE feature. We cannot provide support for third party extensions for Firefox.
I will leave this open as a "wishlist" bug however, because if someone familiar with the ABE feature and the way its rules work cares to contribute an example, we would love to add that to the install documentation.
It should only affect the "add this computer" page, which tries to get your hostname in order to create a human-readable default name for the system you're adding to your account. Once you've added a given machine, I believe you can re-enable ABE.