It would be useful to have an option that logs each time & duration when a student accesses quizzes, tiles, handouts, etc. This would be for keeping track of data that can be used to track student progress with respect to performance (student performance vs. time spent on assignment, etc.), as well as having the info to refer to if students claim they completed an assignment, but the access & submission information shows differently.
I think the primary issue is the fact that "last modified" tracks the most recent edit by student OR teacher. A simple change to adding "last modified by student" and "last modified by TA" columns would make a world of difference.