A small pop-up window to appear after a second (or so) worth of mouse pointer hover over squares/lessons in day and week view. This would save much investigating time (checking if a student is in, then navigating to their timetable) to check where they are/should be.
It would also save considerable time finding out which teachers to target and chase certain register entries (or lack of) for example.
I've mocked up a photo example, attached