I poked around on the NY craigslist, but didn't find an 85 with a 3.8. Anyway, just normal things for a used car. Inspect for rust, body damage, gacked wiring and if it's a landau top car, tap on the roof and if it feels spongy or hollow walk away. G Bodies LOVE to rust out in the spare tire well and the little side pockets in the trunk. Also up under the wheelwells and floorboards. Check the fluids. Check transmission fluid while it's running and in park. If it smells burnt, somewhat like toast, transmission is probably shot or in need of a rebuild. Check tires and see if wheels are bent. Push on the car to see if shocks and springs are noticeably worn out. Test as many interior components (power seats, windshield wipers and fluid sprayers, radio, etc) as you can. Finally, ask to take a quick test drive. Assuming it's a three speed auto (most likely 200c), run it through all the forward gears. Start out in 1st, then move it up to 2nd then D. Test reverse. When stopped of course. Make some wide and some sharp turns. Test the brakes. If they're a bit squishy, but the pedal doesn't hit the floor, or the brakes don't feel like they're gabbing, that's good. I could go on and on, but anything that's not in this little rant is pretty much common knowlege.
****EDIT***** Even if the fluids might look clean, at least to a full oil change with filter as soon as you can. If that 3.8 is anywhere close to 100k miles, the oil pump might be struggling. Just a precautionary measure. Also, if you are able to, since the 3.8 Cutlass's for the most part only had a speedo and fuel gauge and a myriad of idiot lights, get a GOOD set of gauges. The three pod style like you see on the shelf at a parts store. Coolant temp, oil pressure, and Oil temp or Volts are the most common ones. You'll thank me after you do. If I had them, I could've prevented my poor lil 3.8s destruction.