This may be "by design", but I've found it annoying while building for a group. I've noticed that if I drag/copy an object to get a duplicate, the copied version (the object that rezes to the original position) is set with group "None", though "Share with group" status is retained. This means, I have to go back to that object and reset it's group to the group I'm working with. Its annoying when working with single prims, or linked sets spread over large distance.
Yes, it's possible to drag a select box around the entire area and set all of my objects to the group. But, I've found it easy to miss a prim or two in that process that was just beyond selection range. Also, if the auto-return is set very low, it can be an extra pain to keep reselecting the group for obects after drag/copy.