It would definitely be interesting to pick up a Broken Wand of Fire, use it in battle, only to catch yourself on fire. Or maybe a Broken Wand of Teleportation randomly beaming you around the dungeon at the most inconvenient time. But they don't have to be all bad. The "glitches" could help you, as said by Peuo. But if there weren't any benefits to them, the player probably wouldn't use Broken items unless they were desperate. Which could be a good thing.