I would like to block students progress or display a label notifying that they should complete overdue work before progressing on the course. In the current Moodle, this is possible, but would require setting restrict access based on activity completion and picking each activity separately.
I suggest adding one (or both) of these two features:
1) Restrict access if there are any activities that are not completed by expected completion date. This would provide a general mechanism for telling students who are late to go back and complete the late part before advancing.
2) Restrict access by completion date so that students can advance only if they have completed all activities that are set to be completed by a specific date. For example, if I have a course consisting of two sets of activities and the first set would have expected completed dates by end of January or earlier, I could restrict the access to the second unit until a student has completed all first unit activities using the end of January DL as a reference.