1. Make sure it's a real one, LOTS of fakes out there, and they look right, turn it on, you can tell the diference in screen quality, if you can plug it into iTunes, fakes wont connect.
2. Check it's not blocked/stolen/unpaid (or going to be unpaid) contract.
3. Just check it works, sometimes if it's be jailbroken you get a 1015 error when you try to update it on iTunes, sometimes you can fix it, sometimes not, so if the phone is in "Restore" mode (as all new ones are) make sure you can activate it (you can't if it's 1015'd)
4. Don't worry about marks on the back, 2min job to change them, screens/digitizers take a bit longer
5. Make sure the WiFi isn't greyed out, this can mean a hardware fault
6. Check all the buttons work (all = 5, shouldn't take long)