In Moodle 2.2 and earlier using mod assignment, assignments would only be displayed in the course overview block if:

1. The assignment had a due date
2. The student could submit a file / response to that specific assignment (It was not outside of the date restriction, and prevent late submissions was not set)

In the new mod assign all assignments in a course appear as long as they are visible for example:

If you create an assignment (using mod assign) and give it a due date of yesterday and set it to prevent late submissions it will appear on the my moodle page (course overview) block where in Moodle 2.2 this assignment would not be displayed.