1- Let teacher select filters- don't auto fill them (my filter is set to "future assignments" "not published" and I didn't select these features) It makes no sense when a teacher goes to grade. Clearly it would be "previous" and "published". Maybe have no filters prefilled (as this can be especially confusing for teachers that are not good with technology) and if teachers want to filter assignments they can select the options for themselves.
2- Allow a thumbnail preview of assignments the way you can view a google doc in your drive (if at all possible). This will allow me to screen for blank documents that are turned in, and prevent many angry emails when students receive a 0, or points are deducted for lateness, as I can inform them of the error ASAP.
3- Allow students to preview attachments BEFORE submitting. There are many students who submit the wrong document after the due date and need to email me to kick it back to them ( "allow resubmit") so they may turn in the correct item.
4- When students submit from their drive they are still able to edit their document. They tend to turn in blank assignments and do them later/ claim that they had it answered and I marked it wrong. While I can prove them wrong with the google drive view previous formats, it is a pain. Maybe having the google document change permissions or making me the owner while it is turned in could be a solution (I realize that this may be completely out of your capabilities, but just throwing it out there :-))
5-Allow teachers to change classes when in the assignment center (the same way you can in the grade book)
6- Allow options for things on bulletin board or edits on the topics pages to be shared/ updated on several class pages.