The Mirror of Galadirel and the Palantiri

[Gorthaur the Cruel]

These two powerful objects have similar capabilties: seeing from afar, eavesdropping (maybe only the palantiri [?]), and showing visions of the past and future. My question is why Galadriel could not verify that it was Sauron in Dol Guldor during the White Council. Similarly for Sauron (and Saruman), if he had the Ithil stone, why could he not "see" the goings on of Lothlorien and Rivendell and command the palantiri to reveal who the keepers of the Three Rings were. And finally, which was more powerful, the Mirror or the palantiri?

[Inziladun]

While they were similar in their power of showing the viewer future events, I think the Palantíri were more dependable. Galadriel said herself:

Remember that the Mirror shows many things, and not all have yet come to pass. Some never come to be, unless those that behold the visions turn aside from their path to prevent them. The Mirror is dangerous as a guide of deeds.

FOTR The Mirror of Galadriel

Compare that to Gandalf's statement about the Palantíri:

The Stones of Seeing do not lie, and not even the lord of Barad-dûr can make them do so.

ROTK The Last Debate

Galadriel may have dared to try and view Dol Guldur, but could she have been certain if what she saw was accurate?

As to why the Ithil and Orthanc stones were not used to divine the Keepers of the Three, I once considered that in order to look on a place with a Stone, you had to have both an idea of its specific location and its appearance, otherwise you were merely 'shooting in the dark'. Also perhaps if Sauron or Saruman did attempt to view Rivendell or Lórien, the Rings themselves may have been a protection.

I say to you, Frodo, that even as I speak to you, I perceive the dark lord and know his mind, or all of his mind that concerns the Elves. And he gropes ever to see me and my thought. But still the door is closed!

FOTR The Mirror of Galadriel

Actually, it's odd to me that Saruman wouldn't have known already where the Three were bestowed. After all, he had been the head of the Council, and probably had the most knowledge of Ring-lore of any who remained in ME, save Sauron. Moreover, he was considered one of the greatest allies of the West for most of the Third Age.

[Boromir88]

if he had the Ithil stone, why could he not "see" the goings on of Lothlorien and Rivendell and command the palantiri to reveal who the keepers of the Three Rings were.~Gorthaur

Despite Sauron's power, and apparent ability to control the palantir, he was not a rightful owner. He simply relied on his spiritual power to use it, and that is why he loses to Aragorn in their battle through the palantir. Aragorn, being Elendil's heir, was a rightful owner and that gave him an advantage against Sauron when using them...however even Aragorn feared he was not powerful enough and I think he remarks about 'barely' beating Sauron. He was pretty drained after the contest, and I'd imagine Sauron would be too anytime he tried to use an object that he didn't rightfully own.

Actually, it's odd to me that Saruman wouldn't have known already where the Three were bestowed. After all, he had been the head of the Council, and probably had the most knowledge of Ring-lore of any who remained in ME, save Sauron. Moreover, he was considered one of the greatest allies of the West for most of the Third Age.~Inziladun

Well Galadriel had wanted Gandalf to head the Council, so there may have been origins of distrust towards Saruman, but we know Saruman didn't like that and took it for himself when Gandalf rejected the job.

Now, Saruman does eventually guess that Gandalf is one of the bearers of the Three, and this makes him even more jealous of Gandalf. This may also be why Saruman decides to try and make his own Ring, one that he can show off to Gandalf.

[Gorthaur the Cruel]

I just had a thought I'd like to get out there. Now Galadriel clearly tells Frodo that, "Many things I can command the Mirror to reveal." So meaning she could let Frodo or Sam see the past, present, or future. But if she left the mirror to work for itself, it's the strangest and most beneficial vision compared to the prompted visions. So I don't think the mirror is unreliable (when compared to the Palantir) and dangerous if under Galadriel's promptings, but it is dangerous when it's used as a guide for arbitrary visions.
And we all know that Galadriel had to pass a test of pride. Could it be that she knew all along, through her Mirror, of the Ring in the Anduin and within Bilbo's possession but kept it to herself? Because she did hide her musings on what she could do with the ring. She even tells Frodo that not even the wise could perceive her thought more clearly (meaning her wanting the Ring) than he when he offered her the Ring. So is it possible that she let this all go on (hiding knowledge of the Ring's whereabouts but not pursuing it like Saruman) to eventually lead the Great Ring to her? Could it be that she also let these things happen (without telling the Wise of her knowledge/desire of the One) to maximize the lasting benefits of a world after Sauron (death of Smaug, Gandalf kills Goblin King and Balrog of Moria) just in case she'd choose to pass her test?