If you are buying this locally, have the seller install a benchmark like 3DMark on the system and then run it to make sure system does not crash under load.
Look for dead pixels on the screen (A couple in random spots is OK, unless you really want a perfect screen), check keys on keyboard, check that all screws are there and tight, make sure Windows is activated. Check for broken or cracked shell parts, USB ports, lid hinges tight, etc... You may want to bring a USB stick to test ports.