The Item Selection Glitch
Exclusive to the original Japanese release, Hard mode difficulty. The glitch so far can't be used to help the player in any way.
Basics
When you select a restorative item you have three options: Use, Discard or Set. You can consume the item, throw it away or set it as your active item in the item shortcuts (bottom left of the HUD). For any equippable you can select Discard, so long as the item is not equipped or otherwise set to be impossible to throw away. For Omega Reports and G Reports you can select to read any of the collected files.
On Hard mode (and Ex Hard, not available in the original JP release) the game is not paused when accessing the main menu (Triangle) so you can move around collecting items even while inside the Item sub-menu. Though you can move around using the left analog stick you can't jump/roll/shoot while in the menu.
The Twist
If you have selected an item and then proceed to pick up an item that become stacked on a higher step in the inventory, your cursor will move one step upwards. This requires the new item wasn't already in your inventory, as it needs to be inserted into an empty item slot for the cursor to move one step up. The cursor also will not change if you pick up an item that is added onto a lower section of the inventory.
In the post-original releases you will be forced out of any selection menu you were just in if you also pick up an item on the field. Be that the "Use/Discard/Set", "Discard" or the report lists.
But in the original release you'll stay in the same selection-menu while the cursor has now moved one step upward. The selection-menu, in this example Use/Discard/Set, will now apply to the Cardkey [カードキー] even though it is a greyed out item that shouldn't have these options.
Select "Use" and nothing happens. Select "Discard" and the cardkey is thrown away which in many cases will mean the player can't progress through the stage. Select "Set" and the item is added to the shortcut menu, though nothing happens when you try to use it. "Cardkey" stays in the shortcut menu even after using up the actual cardkey, though your new
fake cardkey can't be used to lower additional barriers. Cycling through your shortcut items or picking up items will remove the fake cardkey from your shortcut items.
Because the Item Selection Glitch (ISG) only works for when the cursor is moved one step upwards, you can't apply the Use/Discard/Set option to Omega- and G Reports, ammo, equipment and the Gold Moogle Doll. All the restorative items with the Use/Discard/Set option are at the top of the inventory list and the other aforementioned items are always below the restoratives. So you can't set Omega Reports to your shortcut items, for example.
If you have 0 bullets of a given ammo type and use ISG to remove one more bullet from your inventory the menu will briefly claim you have -1 bullets, but in actuality your bullet count never goes below 0. No means of infinite ammo here.
The glitch allows you to discard items even if Vincent has them equipped. The result is that you can "remove" even Guns and Frames from your weapon slots which is something the game normally does not allow. What you'll quickly notice though is that removing the Cerberus and Long Barrel doesn't actually change any gun traits expressed on the field. The equipment menu HUD might look weird but in essence nothing changes. Remove Sniper Scope after ISG and you still have deep zoom available. Remove Power Booster after ISG and you still have added power.
When you have removed an item from your weapon slot, using ISG, the next addition to your inventory will automatically fill that slot. In this way you can "equip" impossible items, like Mega-Potion [メガポーション] or even multiple Power Boosters [パワーブースター].
Sadly, the Power Boosters do not stack in any way to improve your gun power beyond what's intended. Only your original instance of the Power Booster, before the glitches, will count.
In summary I highly doubt that the Item Selection Glitch will be useful for anything. There would have to be some subtle nuance of the glitch that I have missed. Maybe there is some equipment trait that can be stacked, or maybe some way to make the "Fake Equips" actually count as valid, but so far the research reveal no such exploits.
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EDIT: The only potential "use" out of ISG is that it effectively expands your inventory, albeit temporarily. By discarding an equipped item you leave extra room in your main inventory while still enjoying the benefits of the equipped item you threw away. But this only applies until you change the equipment slot, after which the discarded item is permanently gone. Confusion would also easily arise from the equipment menu displaying new "fake equips".
Shop Tangent
I had hoped that the shop would display its own version of ISG but that turned out negative. When accessing the shop Vincent is frozen in place, but an enemy may still nudge Vincent to pick up an adjacent item on the field while in the shop, which is how I was able to confirm that no shop counterpart to ISG exists.
The holy grail would have been to find a way to sell restorative items down to a negative amount. If you have -1 Potions and less than 70 gil, selling the Potion will actually remove 70 gil from your wallet and underflow your gil count to the natural max: 99'999'999. But alas, the shop could not be fooled to acquire items neither below- nor above the intended item caps.
