I never understood why people complained about quest item turn-in being clunky until I realized there was a Hard Mode, and if you're using a gamepad, that's the only one the game tells you about.
Here's what you're presented with:
If you're using a mouse, maybe you're trying to find & select the item out of your inventory. And all those icons are the same. If you're using a gamepad, it tells you to press the confirm button (mine's a 360 controller, if you're using a PS3/4 controller, that green A is the X button icon). If you do that, this is what you get:
Same thing as the mouse. You've got to find the right one and click it if you do that.
Don't do that. Instead, in the Item Request window, either right-click (for mouse users) or press the Square/Map/Subcommand button (for gamepad users) on the item to be turned in. Then you get this:
The item you need to turn in is selected, it's the only one selected, and you just click and go, no choosing. If an HQ item is what's needed, and you have NQ, it picks the HQ. If you can turn in either HQ or NQ (e.g., a leve), you can pick either one.
Edit: And from posts further on, if you end up in the inventory window anyway (after spamming Confirm on the controller), you can Cancel once to get back to the Item Request window and do it this way from there. So it's spam X until window changes, Circle Square X X. That's still faster for me because by the time I'm doing these quests my inventory is generally a mess. XD