Things off the top of my head: -
1. It isn't locked with an unknown lock code
2. It isn't SIM locked to any network - try your SIM in it
3. It charges when you plug in the USB charger
4. Switch it fully off and see if you can switch it on again (check for boot bugs)
5. Check screen calibration and vibration
6. Check to ensure you can switch on bluetooth and the FM radio
7. Play some music and see if the volume keys work
8. Check if the headphone socket works.
9. Use the camera to take a picture, ensure you can view it afterwards
10. repeat above for video
11. Switch the GPS on and see if you can get a lock
12. Open a command shell or text editor and see if all the keys work
13. Make a call to see if the phone works, and that the other person can hear you!
14. Check the WiFi works.
15. See if the screen auto-dims when you cover the sensor
16. If possible, check the notification light works for received call/text

I think that's most of the hardware checked out... any software issues should be solvable with a full reflash....