It seems there is quite a few users have problem with the rattling jack/plug where the cable connecting to the ear cup, here is a simple fix that worth trying.
All you need is a tiny bit of blu-tack or similar matter.
1. Cover the black part of the jack with a thin layer of blu-tack, too much the jack won't fit.
2. Connect the plug to the the headphone and push with a bit of force. You should see the excess blu-tack get squeezed out.
3. Remove the excess blu-tack with finger nails or something, enjoy your MDR-1R without the clicking sound.
Perform this modification at your own risk. I am not responsible for any damage that may occur.