Chris - eyeteeth is right, the bushings that usually need replacing are the ones on the far right and left in your picture.
I think a nut or screw on the motor shaft came loose or off, allowing the motor shaft to turn freely inside the linkage mounting hole.
The hole you circled is where the wiper linkage mounts to the wiper motor.
See this picture at http://weblink.carquest.com/acl/?mfgName=REB&partNumber=40-394.
The silver metal part on the linkage in your picture is the wipers crank. It translates the rotation of the motor shaft into the linear (back and forth) movement of the linkage. (The basic action is similar the the crankshaft/connecting rods in your engine.)
The hole you circled has flat sides that mate to flat lands on the motor shaft. This is so the silver metal part of the linkage rotates with the motor shaft.
