Missing prongs on rings. The model treats thin metal prongs as background because they are thin. Use the restore brush in the manual editor to paint them back.
Diamond edges cut off. Diamonds have hard edges that contrast with their surroundings, but the bright specular highlights can confuse the model. Check the result carefully. If the diamond edges are rounded off, use the manual editor to restore the shape.
Chain links disappear. Fine chains have repeating small holes. The model can treat the holes as background and remove them. The fix is a very tight crop with a lot of resolution on the chain, plus a high-quality model.
Reflections look wrong. If the original was shot on a coloured surface, the reflections pick up that colour. Either reshoot on a neutral surface, or accept that reflections will look slightly off on non-matching backgrounds.