I have a 2000 f250 crew cab v10 4x4 that has a lot of play in the drive line or suspension .when I take off or when I stop you can feel it after that it is normal .the drive shaft at the carrier bering moves up and down and side to side ,is this normal and if it is what else could it be? the trans mount looks good .I just got this truck so I dont know what a good one is feels like but
I know this isn't right .I had an 89 chevy that did a similar thing (rear springs loading and unloading )on start and stop but not nearly as bad as this .this is verry bad passangers ask wht was that on every start and stop.

 

Sounds like a bad carriar bearing and check the u-joints as well.