I just bought a Norinco M14 with a GI bolt already installed. The seller bought the gun from an estate. He does not know who did the bolt conversion. Is there something specific I need to look for to ensure that the conversion was done correctly?

I'm not a gunsmith, but I've had M1As for almost 40 years and did a PolyTech bolt conversion (used an H&R bolt) myself.

You need to check the headspace, or have it checked if you don't have a set of gauges of your own.

You need to look at the wear patterns on the back of the bolt lugs on each side of the bolt.  They need to be fairly even.  The contact between the lugs and the receiver need to be pretty much even to insure both lugs are supporting the strain/pressure of firing rounds.  If you can't see the pattern very well you can remove the bolt, use a sharpie (I used a black one) to mark the back side of each lug and the reinstall the bolt.  Once you've got it together you can work the bolt rearwards and forwards with the operating rod 15 or 20 times and then remove the bolt again and check for how much black ink was removed from the back of the lugs.

If it's not fairly even you might want to have it checked out by a gunsmith.  The bolt may need to be lapped to the receiver.  It's not hard to do, but takes some more "gear" and work to make sure it's done right.

Good luck.  Hopefully everything is good to go and you've got a nice shooter there.

Look and see if it's a reweld bolt. I had a polytech that Elmer Ballance did that had an Hr reweld. I never had a problem with it, some people worry about them not being strong.

All of this plus; make sure the bolt does not contact the barrel shroud.

Check the chamber to see if someone reamed through the chrome lining at the front.  Sometimes smiths will ream out the chamber with a carbide cutter to fix short headspace.  This is very bad for barrel life.