Agreed- this is a substantial oversight, and evidently one that's been going on for years without being addressed despite continuous requests from users. You still can't even manually set the orders to fulfilled.
The orders that we have problems with are already marked as "fulfilled." IIRC, the problem is that they are also marked as "open," which means that they also add to the count in the little number bubble on the left top showing the number of orders to be dealt with, and show up when one filters for "open" orders.
5 years later and this issue is not resolved. this is insane @Shopify. your mission statement is in direct conflict with this issue. "Make commerce better for everyone, so businesses can focus on what they do best: building and selling their products" this is clearly a hindrance to hundreds if not thousands of your businesses. Your solution to me was to hire a custom coder or Shopify expert to resolve this issue. as a small business, my focus is on growing my business not fixing a major error in your backend.
I cannot BELIEVE that I searched this issue that has been a complaint since 2017, and NOTHING has been done to fix it???? All of my highlighted orders are partial refunds as courtesies to customers. In my case the orders are ALL fulfilled and shipped. I need for this to go away because it is extremely confusing to log in and think that you have pending orders, but you are seeing orders that you have already remedied. Just not user-friendly at all. That fact that Shopify has not fixed this is a real disservice to its customers.