Check to see if the following are in order:
Valid airworthiness certificate, current registration, operating limitations/placards, weight and balance with current equipment list, pilot's operating handbook.
Engine and airframe logbooks. Check for complete maintenance history, airworthiness directive and service bulletin compliance, and also entries that suggest repairs due to an accident or incident.
Title search. Insist on one to ensure there are no liens against the aircraft that may affect financing or your ability to sell the aircraft.
Is it clean and dry? Be wary of a spotless engine compartment that may have been treated to a "spray paint" over haul. Check the source of fluid leaks.
Baffles. Eroded, misshapen baffles may be a sign of improper engine cooling over an extended period.
Induction/exhaust systems. Check for corrosion, leaks, worn gaskets, and loose connectors.
Cylinder compression check.
Horizontal and vertical stabilizer attach points. Check for play and loose rivets.
Elevator/stabilator attach hinges. Examine for excessive play in worn hinges. Replacing them can be very expensive.
Rudder trailing edge. Look for dings (minor dents) or putty that would indicate hangar rash and potential control problems.
Wings, ailerons, and flaps
Look for wrinkles, warps, and chafing rivets. Pay particular attention to clean, freshly painted, or waxed aircraft. It may be more difficult to spot problem areas.
Look for dings that may have to be repaired on leading edges of wings and trailing edges of ailerons and flaps. Check the undersides of wings near jack points for dings. Check wingwalks or strut steps for dents, corrosion, and worn-off rivet heads.
Fuel caps and drains. Look for fuel stains around seams, rivets, and wing roots. This may indicate leaking tanks or bladders or, in a wet wing, leaking sealants.
Doors, hinges, and latches. Are all hinges in place and free of rust or corrosion? Do doors close easily and with a tight seal?
Skin. Look for wrinkles or warping. Some "oil canning" is acceptable.
Belly. Look for scrapes, dents, replacement panels, and patches that indicate a gear-up landing. While gear-up landings that result in minor damage need not affect the value of an aircraft, the logbook entries should reflect the repairs.
Antennas. Are they properly located for best reception and transmission? Is the fiberglass coating eroded? Have all antennas been mounted properly?
Struts. Check for leaks, proper extension of struts, and integrity of hardware.
Brakes. Check condition of discs and rotors. Don't forget to test the brakes to see if they are effective.
Tires. Are the sidewalls dried and cracked?
Cabin or cockpit
Seats, tracks, backs, seat belts, and shoulder harnesses. Check for wear.
Instruments and avionics. Test them all thoroughly.