What is the obligation of a Rabbi to be Right?

In our times being devoid of Kings, a Sanhedrin and and Prophets (Hashem Rachamin on his people) the Rabbis of our generation are whom we turn to for guidance. What is their obligation to be right and what is their responsibility if they are not? For example, it appears obvious that the gadolim of the generation of the Shoa were wrong in telling their people not to leave Europe to go to Palestine during the days when it was easy to get out.. Now in our generation, we are given directions by some Rabbis "that it is OK to give away eretz yisrael for Pikuach Nefesh".. or we can live with our Arab neighbors etc... What is a simple Jew supposed to do.. and whom do we believe?

The obligation of a rabbi is to be wise, learned, thorough, responsible, G-d fearing, and to answer questions that are within his area of expertise. A Jew knows that there is no doctrine of rabbinical infallibility. In the case of Eretz Yisrael, ALL rabbinical opinion has seen ceding parts of the Land as prohibited. You are correct that there were rabbis who felt that this prohibition was overrided by individual pikuach nefesh. The events of the past years have forced them to reassess the situation even though their halachic opinion- that individual pikuach nefesh takes precedence over Jewish sovereignty in the Land- remains unchanged. There are many poskim who believe however that Jewish sovereignty in the Land overrides concern for indivdual (as opposed to national) pikuach nefesh.