How much slop is too much?
There are multiple "slops" that you are looking for:
1) U-Joint slop: If you can see movement with the naked eye in one or more of the caps by rotating the DS or moving it laterally, then it is too much and it will continue to wear and will become looser. I have seen a u-joint lose ALL of its needle bearings in two caps and still operate, albeit, with a lot of vibration and noise. Vibration in a DS can eventually take out the bearings in the adjoining components (pinion or transfer case output shaft). Usually, by the time you can hear it or feel the vibration, the needle bearings are gone in one cap. (Note, there are (2) axis of lateral movement that need to be checked. One for EACH "axle" of the cross of the u-joint) Do this for EACH end of EACH DS.
2) Pinion bearing slop: If there is any lateral movement in the pinion bearing, then you will be leaking oil from the pinion seal. This can also give you some noise during acceleration or deceleration. If there is linear movement, then your pinion bearings are loose. There is usually a few thousandths of movement allowed here (like 0.003" to 0.010")
3) Transfer case output shaft bearing slop: If there is any lateral movement in the TC output bearing, then you will be leaking oil from that seal. This can also give you some constant noise while driving and is less likely to be noise during accel / decel because it is a laterally loaded bearing only, not a linear force like a pinion.
When you rotate the DS, you will feel the addition of all the gear lash (of the pinion, carrier, and axles) and the pinion slop. When you feel this, you must also look for lateral movement. If the pinion flange moves forward and back (linear motion) while you rotate, then your pinion bearings are too loose and you have too much gear lash. There will also be lateral movement, just maybe not enough to see or feel yet.
If you have lateral movement, that will be either u-joint wear or pinion wear.
As far as giving a numeric "acceptable limits" for any of these, look in your respective FSM. Those tolerances will be far tighter than what I'm describing here.
So many times, people are complaining of a vibration or noise when accelerating or decelerating or when they are driving that they have a vibration and as soon as they let off the gas it goes away (or gets worse). They reply: "I checked my DS and they are tight!" When I ask if the drive line was loaded or unloaded, they have no idea what I mean. If you have your truck parked on a slight incline, in park, you grab the DS and twist, turn, or shake laterally, neither you, nor Mongo, are going to be able to feel the slop in the drive line. Most people, after I have explained to them what I mean, go back and find that one of their u-joints is missing most of its needle bearings and is very loose.
