Some easy Checklist improvement ideas:
Start Date - Checklists can be created in advance, but like Announcements they get held in abeyance until the Start Date when the email gets sent and they become visible. Events have a similar feature, specifying the invitation date.
Reminder Date - A date or number of days before the Due Date when a reminder email is sent. Events have a similar feature. No need to remind those marked completed already.
Expiration Date - A date or number of days after the Due Date when the Checklist becomes inactive and no longer appear, even if incomplete. Things can only be past due for so long before it becomes obvious it is not going to get done.
The Your Assignments page could be improved to divide them into “Incomplete” and “Complete” assignments. Over due items might highlight the Due Date in red or something.