No inventory control.
Display is exactly as it is in the database. The items are listed related to the order but some have a "0" quantity just like you're seeing in the screen shot.
Yes I tried the exact same items in the cart. I tried entering a "0" and updating. I tried adding from the detail page with a "0" in the quantity. In both cases it doesn't leave the item in with a "0", so it behaves as it should. I can't reproduce the effect.
LITERALLY JUST GOT EMAIL FROM THE CLIENT AS I WAS TYPING WITH WHAT APPEARS TO BE THE ANSWER!
They just realized the items causing the issue were a "by the pound" candy item. If the customer orders 0.5 lbs, the shopping cart handles the decimals fine and computes everything properly. However when the cart writes to the DB, the qty field is set as int(11), so the decimal value gets dropped and the value goes to zero. Then when the order shows in the admin, it shows the zero and things don't total up.
So... the solution would seem to be simply changing the qty structure to decimal (10,1). Can you think of any reason that might cause problems elsewhere in the cart system if the qty was no longer an integer value?