What kind of damage would it possibly do? It idles extremely rough right now and if that's the case that could be the whole reason why it's not running right.You have three possibilities here, and they are equally likely, unfortunately: first possibility is that the new timing tab isn't exactly like the old one and that's the discrepancy. Second is that your damper is not the original, and isn't right for your new timing tab. Lastly, it's possible that the damper's elastomer has slipped, and the weight ring is not lined up where it's supposed to be!
If my eyes aren't deceiving me, the rubber elastomer on your damper looks to be sticking out quite a bit... it would normally be flush. I think I'm going with option 3, and if that's the case, you need to replace your damper before it starts doing damage to your engine.