I would start with some examples that most people know and perhaps can relate to. Take Mordechai, for example. He appeared to do everything wrong, against the common wisdom, but was right in the end.
Shushan's Jews, politically-correctly, attended Achashverosh's feast. (It's not PC to refuse a king's invitation to his victory celebration.) Mordechai, however, warned against it (spoil-sport, not cool, old-fashioned).
Later, when it was time for everyone to bow to Haman, again Mordechai "just doesn't get it." By his refusal to bow, he seems to be the one who brings a death decree on all the Jews.
Indeed, however, as the Talmud says, it was attending the feast, given in celebration of the non-rebuilding of Jerusalem, which brought about the decree. Listening to Mordechai could have saved a lot of trouble!
Let's go on in the story. After Haman's decree became known, the Jews said to themselves: "We have a sister in the palace, Esther. Queen Esther will work to annul this bad decree." What would common wisdom say? "Let Esther tell the king that she's Jewish and we Jews will get favorable treatment." But again, Mordechai seems to miss the boat, instructing Esther to remain silent about her background. What could possibly have been his motive for this bizarre move?
We all know the end of the story. Precisely because Esther did not reveal her Jewishness, the Jews gave up on her and turned their eyes toward Heaven alone, fasting and repenting. This was precisely Mordechai's intent and is the only thing that saved us.
We see that basically everything Mordechai did -- although sometimes seeming to run against common sense -- in the end brought good to the Jewish People. From where did Mordechai get this special insight and ability? From his sincere and total immersion in Torah study; Mordechai, as one of the outstanding Torah scholars of the generation, sat among the foremost of the Sanhedrin, Israel's Supreme Torah court.
Another example is Moshe: When he went to Pharaoh the first time -- at God's command, no less -- things got worse(!) for the Jews. Obviously, Moshe was imbued with supernatural insight, and the imperative to follow him was not lessened by the immediate result of his actions. Of course we all know the end of that story and that Moshe eventually succeeded in a big way.
Note that, according to the midrash, 80 percent of the Jewish People were not willing to leave fertile Egypt for the uncharted dessert. Because these millions of people were not ready to follow Moshe, they were forever lost to the Jewish People.
I think these examples show fairly clearly the importance of following the guidance of our Torah leaders, and that such allegiance should not hinge on our short-term perception of the immediate result of that leadership.