There is a batch delete function. After you navigate to your uploads and you're looking at the files you want to delete:
(1) Click the square directly above or below the individual file squares in order to select all of the files on the page.
(2) If you don't wish to delete all of the files listed, click in the square beside each file that you wish to delete.
(3) Click the drop-down box at the bottom of the page below the list and choose "Delete Rejected." Don't worry about the fact that the files haven't been rejected by an inspector.
(4) Click the "execute" button. You'll see a pop-up window indicating that the files are being deleted. After the operation is completed, you can close this window.
If you wish to confirm that the files have been deleted, refresh the uploads page. I've deleted files this way successfully on several occasions.