When I tap the checkboxes next to items in your Reminders list to mark them complete, I usually want them to go away, so I don't have to scroll up and down, especially when I have a long list of things to do or buy.
To quickly force the marked items to move into the Completed section I noticed that if I slightly swipe to left or right so that part of the next or previous Reminders list appears, then release so that I stay in my current list, the completed items get moved over, and only the uncompleted ones remain.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20120303131642825