[zoltank]

I'm installing a new 4" spindle in my mini lathe. Once it's installed, should I take a very light facing cut on the surface of the spindle to make sure it's square and flat?

[DubMFG]

Yes, you should face/bore your jaws to your machine. But moreover, make sure that your spindle is turning parallel to your bed ways. Using a dial indicator is your best bet, held in or on your carriage. This is also a good time to level your lathe if you have the ability to account for warp in its mounting that can cause you to turn tapers.

[zoltank]

I've checked the headstock alignment before, and it goes me 0.004" taper over 12", which I think it pretty good for a mini lathe.

Roger. Once I get the new spindle mounted I'll just skim it.