When you go look at the cart lift up the axel on one side and spin the wheel, make sure it spins freely and doesn't bind up at all. The wheel should spin at least 3 or four times around with a good yank on it. Mine spin about 6 or 7 times around. Then do the other side. The wheel should spin true , it should not wobble back and forth on the axel, and it should not be warped or have flat spots. Now a little is okay. The wheels should have a slight dish in them, I will have to get a photo to show you what I mean.
Check to see if the wheels are tight on the axel, by taking the top of the wheel and shaking it back and forth to the inside of the cart then to the outside, the wheel can have some play but not so much that it wobbles around on the axel. check the fellows on the wheels, make sure where the spokes go into the fellows they are tight and not split. Make sure where the spokes go into the hubs they are tight too. Check to make sure the metal rims are on tight and the rubber is tight too. What kind of hub does it have? Roller bearings or standard? Ask when or if the bearings have ever been checked, doesn't really matter but you will want to know for maintenance.
If you are refinishing the cart you will probably want to replace the shaft, straight heel shafts are not that expensive and I think you can order just one.
I have a cart that the shaft is fixed with a muffler pipe, and it has lasted for years, but check that out before you use it. Check the balance of the cart, make sure you like the way you get in and out of it and you are okay with that.
The wheels are the most expensive part of the cart, so really check them out.