First, I check to see that the stem and seatpost are not seized in the frame. I look to see if the seat post collar looks to be in good shape or looks deformed/chewed up (sometime people put the wrong size seatpost in and crank down on the bolt to hold it in place). Then I inspect the down tube and top tube junctions with the head tube and look for bulges, indicating a front end crash. I will also run my hand over those areas, sometimes those things can be felt easier than being seen

I inspect the bottom bracket area where the the tubes intersect for cracks/corrosion. I check the rear drop outs and their junctions for cracks. Then I view the whole bike for dents and stand back and look at the fork and make sure it is not bent. I hope that helps. Most bikes are fine. Every so often, issues crop up. Even when they do it isn't always a deal breaker, I just want know as much as I can and factor it in when I make an offer.