Hey Luke. Thanks for checking out the project, really glad you think it's interesting. 

> Is each authentication via Steemconnect unique to the domain where Finally is installed or is someone always logged in to any site that uses Finally?

Finally is loaded in an iframe so the login state persists across all sites that use Finally.

Just tested and fixed the issue you noticed (https://github.com/code-with-sam/finallycomments/pull/29) thanks for sending the error message.