So we can better narrow down the issue, please answer the following 5 questions:
1. Which browser (and version of) are you using? Visit http://supportdetails.com/
Firefox version 19
2. Which username were you logged in to when you commented?
3. What is the URL of one of the posts you commented on? (only one, please)
4. Are you able to see the notifications as expected at http://wordpress.com/#!/notifications/ ?
Negative, endlessly loading icon on blank screen but nothing appears
5. If you expected to receive notifications via email, did they arrive, and did you check your email's spam folder?
I have no e-mail notifications active but have been using the toolbar icon which changes to orange when a new reply is made, providing a dropdown box for reading the reply and making a reply to it. This is not functional.
We'll look into this, but we'll need specific answers to all 5 (no shortcuts, please) before proceeding.