UPDATE: Version 2.2 has been released and improves the look and feel of the note within Gmail, adds an "Add Date" feature, and brings an option to "Unauthorize" Gmail Notes from accessing Google Docs (on the Options page).
UPDATE: Version 2.1 has now been released and brings with it some changes to the User Interface. Instead of inserting a Gmail Notes widget for sign in and adding a note, an icon in the address bar will bring up a sign in popup and allow you to add notes. This was done to make the extension work better for Google Apps accounts and also makes the extension behave the way Google intended extensions to behave.
Numerous bugs were also fixed that should make Gmail Notes less picky about the URL and perhaps even run on Google Apps accounts (this hasn't been tested and will likely have bugs).
Please post all bug reports and feature requests in the comments.