I am not sure of the years of production, but weren't the early 1873 Winchesters made with cast iron receivers? If so, I would want to make sure I got one with a steel receiver. Beyond that, inspections on older lever actions follow the same rules as other rifles:
* Bore- since the cartridges these rifles were chambered for were loaded for many years with black powder, I would make sure the bore is not corroded, then see if you can get the owner to let you disassemble the rifle to check to see if the date stamp on the barrel matches the serial number's production date and the chambering matches the original production records.
* Lever- No undue wear, no slop in the pivot pin, no pitting (or not an unreasonable amount) from sweaty hands on the inside of the lever, link pin not worn out. Ask the current owner to remove the side plate so you can inspect the internals, including the toggle. Sideplates were marked with the serial number on the inside surface.
* Carrier- carrier not sloppy in the ways, no side-to-side movement.
* Bolt- Bolt ways not oversized, bolt corners sharp.
* Hammer- Original hammers had the little checkered portion cast into them, so the checkered area had a border around it. If the checkering goes clear to the edge, the hammer is probably a replacement. Make sure the rifle cocks when the lever is cycled. If not properly lubed, the hammer can wear to the point it will not cock.
* Wood- wood not soaked with oil at points of contact with the metal (makes wood soft), no black stains around metal (means wood has been wet, probably rusted or corroded underneath), fit on receiver and tang very close, buttplate very closely fit, not undersized or oversized, no splitting at the tang, no splits in the forearm.
* Shooting- since you are buying a shooter, ask to shoot it. Evaluate the trigger and the action, and make a note of the loads used to fire it.