Daas Torah means that the Torah trains a person to think a certain way - with logic, with accuracy, with wisdom. And - and this is the main point here - it is not possible to attain this type of thinking unless you are a Torah scholar. This is because Torah is the way Hashem thinks. Hashem's thoughts are not only wise, they are "perfection." You can only train your mind to approach G-d's way of thinking by studying it. It is not duplicated anywhere.
The Halachic source for Daas Torah is a SMA is Choshen Mishpat #3, where he writes that the Halachic rulings of the layman tend to be the opposite of those of the Torah.
Rav Chaim Brisker gave numerous examples. Here's one:
He asked educated, clever laymen what they think the Halachah ought to be in a case where your cat drinks up your neighbor's milk (do you have to pay for the milk)? And, what is the Halachah where your son accidentally throws his baseball through your neighbor’s window (do you have to pay for the window)?
He gave a hint: In one case you have to pay, in the other, you don’t.
The laymen said that of course if your son breaks the window you have to pay - you can control your son, but not your cat! Parents have an obligation to make sure their children do not break windows, but there is no obligation to train cats.
The Halachah is exactly the opposite. Your cat is considered your possession, your property, and therefore an extension of yourself. You property damages something, it’s as if you damaged it.
But your son, although there is a moral obligation to teach him right from wrong, legally, he is still not your possession. Therefore, you cannot bring the father to court for the deed of the child. They are two totally different entities.
There are more like this, but the point was, the Torah teaches people to think clearly, properly, and wisely. It also teaches values that are integral in making decisions.
Therefore, the greater a Talmid Chacham you are, the more you understand Torah, that is, the way G-d thinks, the more you are trained in that way of thinking.
Of course, this is all relative. Who has reached that level where his thinking mimics that of the Torah? Obviously, no human being can reach that level completely, since nobody can be perfect like G-d. The gauge to measure how much "Daas Torah" an individual has does not exist. Today, we have no Neviim, no Chazal, no Rishonim, and no Talmidei Chachamim on the levels that existed not long ago.
The question, "What level of Daas Torah exists today"? Is not one that can be objectively answered, since there is no units of measurement for Daas Torah. What we do understand is, that the Torah thinks differently than we do, and that those who are more connected to the Torah think closer to the Torah's way than those who are less.
And it takes more than just knowing Torah. Outside influences also affect a person's Daas. If his mind is influenced by secular thinking, that effects his Daas. If his righteousness is not proportionate to his Torah knowledge, that also effects his Daas. A person's Midos affect his Daas - if someone is not fearless and independent, then he will be influenced by the masses, the way Shaul HaMelech did not kill Agag because he was afraid of what people would say.
If a person has a vested interest in something (a Negiyus), that also effects his thinking. Nobody is immune to Negiyus. The Sanhedrin Hagadol was vulnerable to Negiyus. The leaders of the Sanhedrin, even in the days of Korach, rebelled against Moshe Rabbeinu, because they benefited from financial favors of Korach.
Even the greatest Tzadik can be misinformed. With lack of information, or false information, even the greatest Daas Torah can be terribly mistaken.
And even after all that, nobody is infallible. One of the reasons for the Halachah of "ain onshin min hadin" - that we do not punish people based on a Kal Vachomer - is because a Kal Vachomer is not a tradition but rather logic. And you never know for sure that your logic is not mistaken. You have no right to punish someone else because your logic says he is "chayav." That applies to the Daas Torah even of Chazal.
In addition, there are other factors that can cause great Tzadikim and Talmidei Chachamim to make mistakes. Sometimes, as a punishment for the generation, Hashem will blind the eyes of its leaders, and make the greatest Talmidei Chachamim say the wrong things. This, according to the Maharsha, is why Rav Yochanan ben Zakai "forgot" to ask Aspasyonus to spare Jerusalem. Because the generation was not worthy, Hashem hid the obvious and logical from their leader.
The Torah leaders are spiritually connected to their flock. If the flock is not worthy, the leader is blinded. Even the prophecy of Moshe Rabbeinu, Chazal say, was only for the sake of the people, and when the people were not worthy, Moshe lost his Nevuah.
The Ohr Hachaim says that the reason the Meraglim[spies sent by Moses] got so messed up is because even though their (the Meraglim) intentions were pure, but - listen to this! - because those who elected them to the job had the wrong intentions, the character and the imperfections of the people infected their appointed representatives - the Meraglim.
In other words, if you are a Tzadik but elected to your position by non-Tzadikim, then you are in trouble of getting messed up yourself.
