I can see why he'd want to look at it himself. Units like those are now selling for less than an Apple visit and repair would cost.
I use Scannerz. It's the only tool on the market that can catch those types of problems...or at least the only tool on the market that's affordable :-)
In any case, I haven't worked on a model specifically like yours but I've worked on models similar. Assuming yours is similar (iFixit.com has step by step instructions for your model...I just checked) the airport card isn't on the logic board, it's located in the back of the display unit under the clutch cover. You would need to check primarily for making sure that the Airport card is seated properly in the cable and connector. Unfortunately, the cable itself feeds into the logic board through the junction between the display and the base, and can be susceptible to breaking because of the constantly opening and closing of the lid. On older MacBook Pro's the Airport was on the logic board and if the screws and Kapton tape have come loose for some reason the card would tend to pop up and you could get erratic connections.
If you choose to open it up, I would do the following:
Don't bother with the Airport card yet. Just check all the connectors that are immediately available, and make sure they're all seated properly. I'd then retest the unit. If errors/irregularities go away, it was probably a connection that's worked it's way partially loose creating an intermittent contact.
If errors/irregularities still show up you might want to go into the display housing and disconnect Airport in them, then, with them gone try and run the tests again. If the problems disappear you've isolated the problem, but I'd bet $50 ($20,000 if I was Mitt Romney - LOL) it's a cable, not the card causing the problems.
If problems still persist it's probably the logic board. There isn't really a "supply" in these things. The real supply is the battery and the charger, and on the logic board there's some minor regulation circuitry and voltage control in that but it can't be repaired to the best of my knowledge. You said the problem occurred using the battery and then using the AC adapter so I think you could rule out spikes from the AC adapter as the source of the problem.
A lot of people may think I'm insane for suggesting these procedures, but a lot of people also forget that not everyone has an Apple store near them, and some people really don't have the money to throw at a new unit.
If you open it up, be careful and gentle, and good luck.