Thrain in Dol Guldur

[Legate of Amon Lanc]

Originally Posted by Zigûr

I almost think it would be typical of Sauron, having taken want he wanted, to have simply dismissed the prisoner with no further thought, even though searching him properly and interrogating him might have actually revealed useful information.

Exactly this. It is a classic trait of Sauron (and indeed of most of the arrogant evil guys in Middle-Earth, or Arda, or Eä for that matter) to overlook the subtler things (and it of course always backfires). During the War of the Ring, Sauron was thinking about Isildur's heir but not about some random hobbits. Orcs in Cirith Ungol weren't much better, even those who had noticed there was more than one halfling lurking around. "Look, this one has a mithril-coat! Yeah, he had an accomplice, but that was some servant who didn't even have a mithril-coat, what a loser."

Originally Posted by Inziladun

Well, Sauron may been interested to know how the Ring had come to Thráin, just to help him keep track of where one of his Seven had been, and maybe piece together any sort of mischief it had accomplished. Probably not much beyond that though.

Also depending on Thráin's state at that point. Once again, in Sauron's arrogance, he would probably see a former king of exiled Dwarves, basically a beggar if not for the Ring, so he would just laugh at him and mock him for being a poor ex-king who had just lost his last valuable possession, the Dwarven Ring (and, if Sauron had paid attention to it, he would probably just laugh how all this Dwarven king now has is a dirty old jacket and a rusty key).

For that matter, Sauron already had all the other Dwarven Rings (those which had not been consumed by dragons; I assume he might have known, given his connection to the Rings and his general knowledge and interest in the matter and all), it is said the Ring he took from Thráin was the last of the Seven (I think Thráin tells that to Gandalf). So it would be an extra reason for him to be distracted after he got the Ring: "Yes! Now I have the last of the Seven! Ha haaaaa! Take this filth away, I have no more use for him, play with him or whatever, I am just going to dance here for some time because now everything that is left are the Three and the One! Ha haaa!"