Oldcar,
Welcome to the Model A world. You chose wisely.
I'm not as experienced as some of these other guys, but these are some of the "biggies" that come to my mind based on my own experience buying my roadster years ago. There were expensive surprises I didn't know enough to look for at the time. And, like a dummy, I didn't take an experienced Model A'er with me or read up ahead of time. I thought, "How hard could it be for an engineer to recognize a 'nice car' to buy when he sees one?!" And so began my education... (very humbling...)...
Some heavy-hitters - not always readily visible and usually costly to correct.
1. Frame condition: Cracked? Doublers/reinforcements welded into place anywhere? Bent or sagging? Heavily pitted and corroded?
2. Underside items already mentioned: I had nearly-seized brake cross-shaft bearings and bent and nearly-corroded-through brake rods.
3. Body and fender condition already mentioned.
4. Brakes: Pedal travel? Stopping distance? Pull a drum or two if seller allows - with your Model A guy looking over your shoulder. Pedal travel?
5. Correct body parts for the year and body type? My roadster had a couple of "incorrect" parts which became a real headache to correct.
6. Invisible engine condition?: Cracked block? (very difficult to detect unless blatantly obvious via leaks, etc.), Blown/leaking head gasket? (Compression test), Main and rod bearings? (noises when driving?), Rings and bores? (Compression test), Excessive valve noise?, Oily exhaust "smoke"?, Coolant out the exhaust pipe?, Pull the dip stick for kicks and see what condition the oil is in - correct level? - clear vs. dirty? 'Says a lot about the seller's attention to careful service.
7. Water pump leak?
8. Starter engage and disengage normally?
9. Type and condition of fan?: If original steel two-blade - needs replacing with new aluminum or other safe options.
10. Transmission and rear end: Leaks? Staying in gear as mentioned?, excessive gear noise- powered and coasting? Fluid levels? Fluid condition? Backlash when going from power to coast?
11. Wheels: Bent? Corroded-through or missing spokes? A couple of mildly-bent spokes could be easily straightened.
12. Grab front wheels at the tops and push/pull laterally back and forth: Loose/worn bearings, spindles, etc.?
13. Smooth or "chattery" clutch engagement on start-up?
14. Generator charging? All lights work? Horn work?
15. Hyd. shock absorbers: Present? Filled with fluid? Working?
16. Steering: Excessive backlash or "deadband" when reversing steering direction? Gear box oil level full? Pitman arm, drag link, tie rod ball looseness?
You may be able to negotiate selling price reduction against any "shortcomings" in the above areas or other "discoveries"! - OR the seller's refusal to let you inspect certain areas! - usually a bad sign...
And studying The Judging Standards and Les Andrews' books will be extremely helpful.
Earle