Should the rear sprocket have some play from side to side.
I installed a new sprocket and it is mounted well.
thank you,

Its a yamaha downfall with the sprocket cush drive system the use & they wear on the hub & wear inside the sprocket holder. If you only have 'Some ' play ya doing far better than me. In my case it's probably the chain guide keeping it inline but never lost a chain because of it. People have variouse ways of reducing the play but in my opinion spacing it hard ove sideways isn't going to end well for the big circlip & doing 'that' only masks the movement. I wonder how a sleeve made to size would work. Sking the sprocket holder inside & skim the hub. But then that reduces the circlip depth as youd need to machine it all the way out to get the sleeve on. Just live with it i guess & grease under it now & then.
Very first DT1 had a bearing in the sprocket carrier. Must've been too costly to manufacture. I've got a TT250 wheel waiting for me which has 'that' bearing in the sprocket trick--good trick 'that'.

I thought I read somewhere that the slight side to side play was deliberate so that the sprocket could self-align in the chain in the event wild things were happening with the suspension and chain tension?

Call it racing clearance, but there has to be a limit, & the circlip will tell you that if it twists & pushes too hard.

Thank you very much