What evidence would you want to see publicly to be convinced?
I would not necessarily need information to be publicly published in order for me to believe that someone is satoshi. If someone were to ask me to keep evidence private and were to personally see sufficient evidence (whatever that may be) then I would be convinced.
If someone who I trust were to publicly vouch for someone being satoshi
and I do not see any problems/issues with what details they provide then I would believe they are satoshi. The problem that I see with the details that Gavin provided is that it appears that he used a computer that was provided by Wright which implies that it may have been compromised.
What information I would want to see personally would really depend on my observed interactions with the person claiming to be satoshi. If someone claiming to be satoshi were to offer one very specific piece of evidence to support that they are satoshi then I would probably be skeptical and want to see additional verifications/evidence. On the other hand, if I were to personally (or if someone who I trust -- eg theymos -- were to personally) ask for a single specific verification then I would be more believing.
I would want to acknowledge that there is the possibility that satoshi might have destroyed, and/or otherwise lost access to one or more of his private keys, so his inability to sign a message from any one of his private keys would not automatically veto his claim of being satoshi.
I would say that someone signing a message from the private key for an address strongly associated with an address associated with satoshi would probably make me believe that said person is in fact satoshi.