When I was shopping for mine I drove a few that I walked away from. Here are a few things that I always did and by no means am I a expert, I just thought I wanted everything to work when I bought it.
While sitting still:
1. Test all of the power windows and sunroof.
2. Turn the heat on and make sure it blows hot. Check to see if it blows on the different vent settings.
3. Turn the air conditioning on to make sure it blows cold. Check to see if it blows on the different vent settings.
4. When cranking the LR3, the compressor should run for about two minutes. Make sure you hear it, it sounds like a normal air compressor, just a little quieter.
5. Place the LR3 in reverse and look to see if the outside mirrors tilt down.
6. Raise and lower the supension via the switch located between the gearshift. LR3 should lift in 3 or 4 seconds and lower and level in about the same time.
7. Test the power seats to make sure they work.
8. This may sound stupid to some, but I always like to smell the exhaust. I like to do this mainly looking for a smell thats too sweet or too much of a burnt smell. This kind of gives you an idea about the emissions systems.
While driving:
1. Roll the windows down and accelerate fast. Listen for any out of the oridinary sounds on take off. Also listen for a knocking sound, this could be a control arm issue.
2. Make sure the LR3 dosent pull too much left or right on takeoff. (Alignment issue).
3. Brake fairly hard with your hands off of the wheel. Look for a pull right or left. Also listen for a knocking sound, this could be a control arm issue.
Hope this helps.