My Driver side wiper seems to be slipping, making me think it is not the motor, but something in the linkage to the wiper arm. It move a bit, but does not make its complete pass. Passenger side work fine, except for when it collides with the lazy arm.

Can I figure out how to tighten this up myself?

2006 Elantra

 

The arm is loose where it attaches to the stub shaft that rotates back and forth. You should find a black plastic cap where the arm is attached that you can pry off with a pocket knife blade or small screw driver. Underneath you will find a small cap nut threaded on the end of the shaft. Use a socket wrench to tighten the nut, but don't over tighten and strip the nut. Do this procedure with both wipers in their parked position. A drop of Locktite on the threads before you tighten the nut will help keep the nut from loosening back up.