inspect for cracks, pitting, functionality... pull the slide back, make sure it locks back with an empty mag in the well. then make sure it'll drop slide with the slide stop. then dry fire a couple times.
as for whether or not its stolen (which i'm guessing is actually what you're talking about)... not your concern. just be happy you're getting a good deal on a gun the government will never know you have, and move on with life. i've bought a gun or two from private parties... i've also opted not to, because the seller seemed like a bubblegumin tweeker.
guns are no different than cars, tools, TVs or couches... if you're buying from a private party, there's always that small risk that the item was stolen at some point in it's life. it's really none of your business- only what happens with it after it becomes yours.
I disagree, the history of the gun should be very much your concern. Imagine...In Oregon you can call the State Police and they'll run a check to see if it has been reported stolen. I've bought used guns without checking first, but because of the reasons above I call them in later.
Do you trace the S/N of everything you buy used to make sure it has not been stolen or used in a crime? Skis, electronic gear, appliances, guns -- they all have S/N's that you could trace (with effort) to see if they have been stolen.
I don't trace these things when I'm buying them used from a person who appears to righfully own them.
Just buy it, use it, forget about it.
You can't have both the security of knowing the gun's complete history and ownership AND the liberty of being free from gun registration. Choose one or the other.