This VQmod extension calculates the notification badge number differently (in admin area).
The main badge displays only Pending (Processing) orders + Returns (so only the unprocessed ones).
Number of Pending is now only the really pending ones, so Old Pending minus Completed.
Since it's rarely used, this extension also removes Affiliates from notification box (you can easily remove this feature).

Should work on OpenCart versions 2.0.x - 2.2.x.