My question to the OP, arsenix2001, is has he ever used another snow blower? If so, does the Woods unit run more or less true then another brand (or even another blower of Woods manufacture)?
Considering the auger and sprocket wheel assembly appear to be a built up weldment, that little bit of lateral run out doesn't appear to detrimentally affecting the operation of the unit. The chain does seem to be running mighty close to that bracket just inboard though...I think I'd want a nylon wear block between the chain and bracket.
I'm sure Messicks have other blowers at their store...suggest you ask them (since they're following this thread, they may offer) to view another blower in operation...see if there's the same problem.
As far as the "noise"...any implement running at 540 RPM is going to be noisy...if you had hearing protection, I doubt you'd notice it.
In a machined assembly, you should expect run out of less then .005"...quite a bit less, if one is willing to pay for it.
In a welded assembly (with no post welding turning of the shaft or boring of the sprocket wheel), run out could be considerably greater..easily more then .03".
I don't have a blower, but I have done a lot of QA in assemblies (both machined components and fabricated components). I'm not convinced there's actually a problem, but I'm not the guy buying the snow blower. I do know Woods has been in the implement business for a lot of years and they do make good equipment (my RFM and wood
chipper are both Woods).