A couple of the more important things to look for:
. . Are there any open recalls?
. . Does it have any factory warranty remaining, ie powertrain, etc?
. . Does it have a vibration around 60-70 mph?
. . Has the intermediate steering shaft been replaced?
. . Does the trans have the 3-5-R waveplate issue resolved?
This may seem silly, but have someone sit in the car and turn the key to ON but not start it. Then go to the rear and look at the tail lights. If the brake lights are on but your assistant is not stepping on the brakes then it needs some work done. Next, have your assistant step on the brakes and make sure all 3 light up fully. Then turn on each turn signal and make sure it doesn't "hyperflash". If it does, check for LED bulbs in the rear and/or front turn signal locations and if a light is actually flashing in that location.
The rest is up to you to take it for a test drive and ask if it can be a bit long. Take it on backroads and the highway. Take it to a parking lot (like a shopping mall) and park it like you normally would and see if it has any peculiarities. Drive over some speed bumps and listen to the suspension. Also listen when making several tight circles in the parking lot, in both directions.
Take it on a straight piece of road with nobody around. Get it up to about 40 mph (60 kph) and then press the brake pedal hard and hold it. Do the ABS brakes keep the wheels from skidding? Do you feel the pedal pulsating at a fast rate while holding it down with all your might? (Both of those are normal.)
Check for a spare tire, jack, and jack handle.
Make sure you can hear the turn signal "clicker" in the left front speaker. If not, turn on the radio and select several different stations. Play a CD if it has a player. Turn the volume up and listen for odd-sounding speakers.
Check the AC to make sure it turns on and gets really cold quickly, especially this time of year.
Having the upper hand means that you are in a position to direct the negotiations rather than let the seller do so.
The ... term alludes to an ancient game in which each player in turn grasps a stick with one hand, beginning from the bottom, and the last who can put his hand at the top wins. Its figurative use dates from the late 1400s. http://dictionary.reference.com/browse/upper-hand