Use a magnetic base dial indicator with the stem set up to measure the movement of the ring gear teeth, as close to 90 degrees from the rotation of the gear as possible as you try to turn the ring gear with the pinion flange held rigid. I like to see a ballpark measurement of .010"-.015", but somewhat more isn't bad if there's no gear whine. The backlash can be reduced by moving the ring gear closer to the pinion with the carrier bearing adjusting nuts, but that also changes the wear pattern on the teeth. Doing that to a set of used gears almost always sets up a whine and results in rapid wear of the gears.
The spider gears and the cross shaft can also induce slack, along with the fit of the axle splines to the side gears. None of that will be adjustable.
Jerry
