Iv never really noticed this until now but my rear shock has movement to the left and right if you give it a firm push.

Where it sits bolted onto the linkage it can slide left and right along the roller bearing.. is this how it should be?

Note that i have a F4I shock fitted and all the bearings are in good condition.

 

Sounds like the shock end is slightly narrower than the stock F3 shock end. You could install some washers to take up most of the free play. Don't bind up the shock with too many washers.