hanging side mirror

If the mirror has a ball joint, and that is where it is loose, you should be able to remove the mirror by soaking it in gasoline (or some other silicone solvent) overnight.

One the mirror is removed, you should be able to find a way to tighten the joint. If it has rivets, then small shims can be placed to tighten it. Or you can remove the rivets, and replace with some screws. Some have screws and plastic bushing, the bushings rip, and the mirror gets loose - those you just need to get some plastic washers to replace the bushing.