. . . Sauron returned, but in general he was there to inspire and tutor the
forces of the West, not to scout the forces of the East. I tend to think
Dol Guldur was an exception, and may have been as much about meeting Thrain "by
accident" as about the purported mission.
As for your second observation, I agree that it is difficult to account for the
Enemy's ignorance of the Shire, particularly because of the Witch-king of
Angmar's long residence in the north during the very time that the Shire was
founded. However Saruman was aware of the Shire, mostly because he
observed Gandalf's interest, as described in "The Hunt for the Ring" in
Unfinished Tales.
As someone noted, however, Sauron's ignorance of the Shire is no more strange
than Morgoth's ignorance of Gondolin. Perhaps in both cases such
ignorance is a sign that a Higher Power was
involved.
________________________________________
"‘I think he was a silly little man,' said Councillor Tompkins. ‘Worthless, in fact; no use to Society at all.'
"‘Oh, I don't know,' said Atkins, who was nobody of importance, just a schoolmaster. ‘I am not so sure: it depends on what you mean by use .'
"‘No practical or economic use,' said Tompkins. . . .
. . .
"‘It is proving very useful indeed,' said the Second Voice. ‘As a holiday, and a refreshment. It is splendid for convalescence; and not only for that, for many it is the best introduction to the Mountains. It works wonders in some cases. I am sending more and more there. They seldom have to come back.'"