A new commenting system has been introduced for Google Sites. It appears to be the same as the Google Docs commenting system and while there are some nice features there are a few issues. And not only does it still not allow public commenting, it has also broken the workaround script I wrote detailed here: Add comments or other content using a form.
NB To remove the comment option from a page, go to More>Page Settings and uncheck the Allow Comments box
See also Google's help page: http://support.google.com/sites/bin/answer.py?hl=en&answer=98225
Provided you have Editor or Owner access, just click on the comment box to add a comment. What's new are the Notification Settings:
The settings shown are the defaults set when you add a comment to a page (the text confusingly refers to 'this doc' and 'this document' instead of 'this page' and the help link takes you to the help page for Document commenting!). The options are reasonably self-explanatory.
The picture that appears next to your comment comes from the Google profile of the account you are signed in with (see: profiles.google.com)
You can '+mention' people in comments. Simply typing '+' into a given comment will open a drop-down menu of auto-populated contacts. Select the user you'd like to add to the comment from this list.
Adding someone to a comment will email them a notification containing the comment thread. If that person doesn’t want email notifications, they can always change their Notification settings. You can even reply by email. (If you have been added to a comment and aren't receiving email notifications, you may want to check your email spam/junk folder.)
However, as noted above, there are a number of issues:
Google have started (as of 7 Nov 2012) updating the new commenting system. As and when updates are made, I will update this page with details. Updates will be done in blue.