This is a prime opportunity for skeptics to identify for themselves, ahead of time , the clear conditions where 1) If Wright meets them, they will accept he is Satoshi 2) If Wright doesn't, then they will not A great exercise in avoiding the moving of goalposts, by setting a clear expectation ahead of time.
If Wright can provide signatures or transactions for the original block, he will be accepted as someone special, if not necessarily Satoshi. If he can't, he certainly won't be accepted.
If he can do that, then it comes down to deciding how he came by those private keys. It's certainly good to pre-register standards, but it's also a really hard question; Wright gave no indication of what evidence types he'll be using, so it's hard to pre-judge every sort of evidence he might offer.
My one other expectation would be that he would explain why the "signature" that got him onto BBC wasn't what he claimed it was. If he is Satoshi, it's a damned odd thing to use a faked signature for his basic proof.