Just the tiniest amount of play possible. Also the pinion needs to be able to slide for and aft in the rear diff, otherwise it will overheat the bearings and melt thru the housing. This is the only r/c I have had be so sensitive to diff shimming. My Jammin truggy diffs were bulletproof.
The way I check it is to first figure out how many shims it needs to remove all side to side play. Then I go after the ring to pinion mesh. I use different size shims so telling you how many and which side to put them on is impossible. I set the mesh, tighten it all down and check for binding. Take it back apart....until it is right. I hold both outdrives with my finger and thumb, then rock the center drivershaft back and forth to feel the play. It's a pain but once you set it, you won't need to change the shim settings.
With new parts I would follow the manual to the letter. It's never lead me wrong. The rear diff for some odd reason is prone to overheating the pinion bearings if you butt the center driveshaft up on the pinion tight. I have to leave 1-2 mm of back and forth play as well as the ring and pinion play needed to make my diffs last. New diff housings do wonders, Kyosho or King Headz needs to make an Al. housing for this rig.