Size is important. If the frame is a little small, you can adjust for it, if the frame is too big, you may not be able to lower the seat and/or stem enough to fit you.
Structural damage can be a deal breaker; cracks, corrosion between metal and carbon parts, large dents in aluminum, bad misalignments, etc.
Then there is the era the bike was made. Older bikes with narrow dropouts will be hard or impossible to upgrade to more modern components, though you may prefer your more vintage bike to have vintage components.
The “perishable” parts of the bike, the cables, tires, brake pads, bar tape, etc, are easy enough to replace, and if they are bad, that’s not a deal breaker.