I just had a poke around at that right side and there is a white washer there, it's just been painted over at some point with black paint, which is why the metal looks so thick. There's absolutely no play in the hinge but I'll book it in at some point.
The most common issues with overdue hinge replacement is that the copper bonded to the frame which result in buying a new frame;
The least common is a snapped hinge due to stress.
It's definitely worth doing, first before you do anything else.