Specifically applies to tasks that are shared:
1. Appear on shared lists
2. Are "given" to others

RTM should send additional notifications to everybody who has access to these tasks for any changes, including:
1. Task is completed
2. Task is deleted
3. Task is renamed
4. Tags are added
5. Tags are removed
6. Priority is changed
7. Due date is added/removed/changed
8. Notes are added
9. Notes are deleted
10. Repeat (Recurrance) is modified
11. Task is "given" to somebody new
12. List is changed

The logic is simple. When one is working on tasks, you know exactly when/how you have changed a task. When you have shared/given tasks, there is no way to track any action other than a manual update from the person making those changes, or trying to remember the details of a task and manually checking every one. The problem becomes acute as the number of people or tasks grow.

Additional:
1. The notifications "configuration" can be updated to turn off these notifications.
2. List-level notification on-off setting (eg: do not notify me for tasks in this list)
3. Task-level notification on-off setting (eg: do not notify me for this task)
4. Contact-level notification on-off setting (eg: do not notify me for changes made by this contact)

#1 would be nice so that people can keep the "chatter" of notifications low. #2, #3, and #4 are just additional considerations for specific use-cases.

Also, the notifications can be clubbed into digests that are sent out after a specific period (1-min, 5-min, 10-min, 30-min, etc.). Instant is always welcome for high-velocity teams, but some people may want a summary.

Hope you will take this suggestion seriously and work on implementing this.