Thanks for the suggestion - we'll be looking at ways we can improve notifications in the future.

that would be great -- as well as notifications on whether someone has added you as a contact, and when a shared task is marked completed.

Definitely a must feature for me for shared lists. Otherwise the person I assign a task to won't know about it unless they log in to the site. I want them to receive a regular email (preferably with the task details in the body of the email) in their Outlook Inbox to alert them they have a new task in the system.