Your rear end has a pipe plug in it about half way up (all I have seen are on the back sheet metal part of the housing but there might be some with it in the cast iron gear carrier I guess). Regardless, fill the unit thru this hole 'til full to the bottom thread in the hole and it will be properly filled.
I don't understand where the slop is in your yoke. If it is in the pinion shaft, a very little slop is proper and reflects the pre-set clearance in the gears. If this is the case, the only way to check if it is too much is to expose the gears and measure the lash per motor manual instructions. If the slop is in the U-joint, REPLACE IT! There should be NO slop in it. Regardless, I would go thru the trouble of checking the gears (messy and a hassle but worth the effort). If it is a used unit, as long as you have it apart, check the bearings for burn, pitting, or wear also.
Bearings whine all the time while bad gears whine on power up or breaking.
[ August 09, 2002: Message edited by: firstname.lastname@example.org ]</p>