Hi,
I've got a delivery note that is marked as completed, but that continues to show when I filter "Status not in Completed". I also have a notification that shows on my desktop, probably linked to this same problematic delivery note.

Thanks for correcting this bug, it is quite frustrating!
ERPNext: v11.1.30 (master)
ERPNext Support: v0.0.1 (master)
Frappe Framework: v11.1.28 (master)
Be sure to post this issue on discuss.erpnext.com to raise notice.
Link to discuss and this issue for folks add comments plus a fix contribution.
Here's a similar Purchase Receipt case https://discuss.erpnext.com/t/purchase-receipt-has-notification-but-all-receipts-are-completed/48531/16
Most helpful comment
Here's a similar Purchase Receipt case https://discuss.erpnext.com/t/purchase-receipt-has-notification-but-all-receipts-are-completed/48531/16