The fuse for my right window blows after about 5 times. So I'm going to take apart the door and have a look. Before I do so, does anyone have any suggestions?

Check the wire harness where it passes from the door post to the door, not only on the right door but also the other door on that circut. You didn't state which window was blowing the fuse - front or rear. The windows are fused right front/left rear and left front/right rear. Could possibly be a bare wire that is making contact to ground every so often with the opening and closing of the door(s).

Check to see if the motor is binding up.