If you want a 3800, I would not focus on one car and just decide yes or no. If you look around, you can find many 3800s with less miles for reasonable prices. GM used them in a lot of cars.
Check all the fluids. I look at and smell them to see if they seem OK. Check the oil fill cap area and see if you see any discoloration or residue that might result from a head gasket leak. I also ask the owner if I can floor the car through the 1-2 shift. If there are trans issues, they may show up when the car shifts. It should be smooth with no hesitation or jolts. I take my hands off the wheel to see if the car tracks straight or pulls to one side. I hit the brakes hard to see if the car stops straight without complaints.
Always check the Carfax. It won't always show problems but it may show good or bad maintenance practices and any major items that have been reported. I ask for maintenance and repair records. A conscientious owner will have them. If there are no records, the car may have been maintained and repaired sporadically rather than well maintained and repaired.
Look for paint overspray in the wheel wells, under the hood, under and around the car. Overspray may indicate a repaint done by a sloppy shop.
Turn on EVERY button and switch to check accessory operation. Every window, the sunroof, lights, turn signals, door locks, etc. Open and close every door to make sure they work smoothly and properly. If you do find issues, they are a good bargaining point. Good luck!