Hi cachehunter,
The first place to look is the motor bearings. Can you run the grinder to hear them? Definitely grab the wheel end of the shaft and see if you get any axial movement, there shouldn`t be any perceptible but a really tiny amount, just enough to shuck if you know what I mean, probably on the order of a few thousandths, shouldn`t be a problem.
Another place to look is the pivot points where the head attaches to the base. With alot of use these points will get sloppy. Bushings used to be available for this but I don`t know if they still are. I wouldn`t buy a grinder with sloppy pivots unless I got it dirt cheap and was willing to have a machinist rebush it, and then only if the motor were relatively new.
Next look at the stop pawl. These are only about five bucks to replace but they are often ground off on one side or the other.
Then check the vise to be sure that the plates aren`t sprung or warped. These can be a real PITA to use if they are not close to parallel and straight. They are less than ten bucks each to replace but should be factored in to the cost of the grinder.
Check the cam and shaft of the chain vise for looseness. There is no repair for this area without visiting a machinist but if you only grind one gauge chain you could adjust your vise so that you don`t even need the cam, just hold the chain taught against the stop pawl with your left hand.
If the grinder has a reversable motor, it`s a plus, and if it has a lightbulb get yourself a bulb adapter so that you can use the off the shelf variety bulbs. The adapter should only be a few bucks at a good electrical supply house.
Russ