I'd probably stay away from grease or similar oils for lubricating the linkage. It has hard plastic bushings in it that are more than smooth enough under normal conditions. Grease will act like a magnet and attract every bit of dust and grit to it, causing accelerated wear.
If you use any type of lubricant, a plastic safe dry lubricant like PTFE would probably be best.
If it's stopping partway through a sweep, it's more likely to be electrical than mechanical. Could be the contacts under the windshield, could be a bad connection at the wire plug at the motor, it could be a failing motor.
The reason I say more likely to be mechanical is if it was mechanical binding or whatnot it wouldn't just hesitate, it would jump ahead afterwards when the force overcame whatever type of binding. Also a mechanical issue will more likely show up at either end of the travel when things are changing direction, rather than the middle when it's under constant force and any slack has already been taken out of the linkage.
