How do I mark an inventory item as trash?
I'm not even sure about when it appeared there. It doesn't seem to do anything when I click it. Any idea ?
That indicates the weapon has been marked as trash. If you go to a vendor and on the Buy Screen sell all trash (Delete on PC, Left Thumb Stick on 360), it would then sell this item and any others marked trash. Note that Left Thumb Stick will mark an item as trash on the 360 (presumably on the PS3 as well, ditto for selling all trash) but there is no hot key to do it on the PC; you must use the mouse (just hover over that side of the weapon and the the symbols will appear "greyed out").
Above the "X" is a Star you can click to mark an item as a favorite, though this purely cosmetic.