I would find it very unusual if someone as privacy-conscious as satoshi posted his name and address on a public forum, but I do believe that it contained some identifiable information, regardless which warranted the deletion.
I knew how it's unbelievable that mistake could be made by Satoshi Nakamoto while he always used Tor. But human can make mistake and perhaps, we can speculate that this one is a very rare mistake made by Satoshi Nakamoto.
I'll probably release Satoshi's PMs and logged IPs addresses in ~8 years. This'd probably be of great historical interest. (Though he always used Tor, as far as I can tell.)
2021 edit: I changed my mind: I am not going to release Satoshi's PMs in 2021. See my post
here.
According to the same thread where theymos wrote what he did, threads 1, 2, and 4 still exist but they are accessible to the staff only, not to the general public. Thread #3 is, thus, different from those. There is always room for speculation. I don't think thread #3 was deleted just for testing purposes. It might have contained something that shouldn't have been there. Like I said, we will never know, but it's fun to speculate.
I agree, what traces left by this thread and leaked information is interesting and gives us a room for speculation. I don't know how Satoshi Nakamoto could make this mistake but who knows.