I finally pulled the trigger on a 5D3(refurb), and some L Glass.
What kind of checklist do you usually go thru to prove to yourself that your copy is good,
and don't need to send it back or for calibration right away?
Apart from that, I just check all the ports look ok, there are no dents or scratches, a quick look inside to check the mirror, simple stuff like that. The real test is when you turn it on and start taking pictures. For that, following what Mt Spokane Photography suggested is a good idea.
Bodies I do pretty much what Mt. Spokane does. Lenses I check centering (equal corner sharpness, symmetrical vignetting), AFMA them and check AF consistency (with FoCal), and then I shoot for real.
After charging the battery, learning the controls (if it is a new model, not just a copy of a model I already have), do some test shots of the dog (or if I am lucky my wife and the dog together). There are so many variables that it is hard to test everything - seldom get a new camera before a big shoot. Like to have a month or 2 early, but that is not always possible.
I take an evening to sit down and configure/learn the controls on the camera. With a new lens I'll take some 'real world' test shots in and around the house but nothing involving test charts or the like. Then I'll usually take it out on a foto-shoot the next weekend, always nice to use new gear Any fault should quickly become apparent if you start using the stuff before the return period is over.