Check the headset and bottom bracket bearings.

Stand over the bike, apply both brakes, plant the front tire and push the handlebars backwards and forwards. Can you feel any movement in the headset? Now, pick the front end of the bike up off the ground by the frame, so that the frame and fork are perpendicular to the ground. Give the bars a nudge and see that the fork turns smoothly to the side with no binding (other than what the cables might cause), grinding or rough spots. Do the same thing on the other side. (Or do it on a workstand if you have one handy.)

Put the bike back down on the ground, grab both crankarms and see if you can feel any side/side or up/down movement in the bottom bracket. Then pull the chain off the chainring - let it rest against the BB if there's room, or just hold it in one hand - and spin the cranks. Again, they should turn smoothly with no binding.

If it's a carbon frame, any defect in the paint is cause for concern. It doesn't necessarily indicate a weak spot or crack in the frame, but it could, so I'd either have a trusted bike shop check it over or just pass on it. With a metal frame, if it's cracked, you'd see it on careful inspection, and chips in the paint are just cosmetic.