It would be useful for teachers to be able to see simply when work has been submitted. Right now we have to scroll through each class and each student to get to the work. Would it not make sense to provide a short cut to the newly submitted work on the assignment page after signing in.
I would add that this could be easily accomplished in the Assignment Center as another column before the "Graded" column. A "submitted" column with the number submitted vs. the number in the class would be very useful.