It occurs to me that I don't remember seeing enough obviously-broken-but-still-functional items in fiction and games, so I am sharing some of mine, past and present:
A pair of over-the-ears headphones with the left earpiece held on by a bent paper clip wrapped around the headband.
A large backpack with a waist strap. The part of the buckle on the waist strap that plugs into the other half is broken off, and the adjuster on the strap for the right shoulder has broken - the strap is held together with a knot instead. On close examination, one of the pair of sliders on the zipper closing the main compartment has come off one of the rows of teeth and does nothing.
A pair of boots. The round laces seem to consist of a woven tube around a smaller cord; one aglet, along with a notable length of the tube, has come off, leaving two ends of different sizes that require some ingenuity to tie.
A proprietary smartphone charging cord. The cord has apparently frayed near the plug at the phone end and been wrapped with a generous amount of electrical tape.
A black leather jacket with a black fabric lining. The front flaps have snap fasteners to hold them closed, but the zipper behind them is missing its slider entirely.
A hard plastic water bottle with a loop on the lid for holding or clipping onto caribiners. The lid also has a space where a hole would have fed water into a bite valve for drinking, but the entire bite valve part is missing.
A large reusable shopping bag. The plastic seems to have grown stiff and slightly brittle; a few cracks are visible in the bottom.
A cheap umbrella with a plastic handle. The bottom of the handle has broken off and been bodged back on with a half dozen coffee stirrers laid lengthwise across the split and a generous wrapping of metallic color duct tape.