Rather than go into all the details of rebuilding a diff, I'll answer your question, but really there is a lot more involved than just the free play between the crown wheel and pinion...
Looking at back of diff, cover off, grab the crown wheel with your left hand like you would sort of hold a steering wheel, move crown wheel up and down, that free play I'd guess is about 2mm, but I say that as a guess because I've not ever measured it, I do it by feel.
But....
How is the Crown wheel & Pinion meshing, depth etc?
Rather than me giving a long winded book explanation here is a very good tutorial on how its all done
Differential Installation Instructions | West Coast Differentials
Here is a pic of a P38 diff out of a Defender TDCi that is just about perfect, you can see the contact point is centre both in height and in the heel (outer crown wheel) and toe (centre crown wheel) on the drive side (the sharp pitch side of the teeth. I generally get the slightest toe so as the diff loads up it ends perfect centre. Ideally this is what you are looking for, but dont be overly concerned about getting slight toe. While there are other contact patterns that are considered acceptable, always work towards centre centre.
Getting the contact pattern centre means there is always 3 teeth meshing, one tooth coming on, one tooth full load, one tooth coming off. If meshing is badly off you reduce this. If setting up say a drag car or anything that will dump a huge load onto the diff, you then set up with big toe so again when full load dumps onto the diff it meshes perfect centre.
http://www.aztech4x4.com.au/images/IMG_2319.jpg
Regards
Daz
Rather than go into all the details of rebuilding a diff, I'll answer your question, but really there is a lot more involved than just the free play between the crown wheel and pinion...