While those few members of the Sanhedrin had a reason for their rift with Mordechai, I believe Pirkei Avot 4:6 provides an explanation for why their analysis was wrong:
"Rabbi Yishmael bar Rabbi Yose said: One who studies [Torah] in order to teach is given the means to study and to teach; but one who studies [Torah] in order to practice is given the means to study and to teach, to observe and to practice."
Mordechai lived the Torah by virtue of his high-caliber character, raising of Esther, and service of his people. Learning is extremely important, but it is even more important to actually apply that which we learn into everyday life. If we simply use Torah study as an intellectual or religious exercise, that is all it will be. But if we have the mindset of studying in order to better ourselves - and allow it to positively influence our behavior - then it becomes the ultimate ethical exercise. Not only will we be able to study and teach, we will also be able to use our studies as the primary means through which to become more kind and decent human beings.
The Ramban, or Nahmanides, writes a very poignant letter to his son in which he lays out an approach to improving a myriad of character traits. This letter is famously known as the Igeret HaRamban. There are even some Jews who try to read it once a week, following the instructions Ramban gave to his son. Toward the end of the letter, he writes:
"When you rise from study, ponder carefully what you have learned; see what there is in it which you can put into practice."
There are many ethical lessons to be drawn from a variety of topics. For example, we are taught that the Mizbeach (Altar) had a ramp so that when a Kohen walked up to perform a sacrificial service, he would not expose himself; the ethical lesson we can take from this is that if we are to have respect for an inanimate object, how much more so should we have respect for living beings created in the image of God. When we do our best to ponder the practical application of religious study, we can often find lessons that will improve our character.
In this light, the Vilna Gaon makes an insightful observation: the Torah is like rain - it gives growth to both poisonous weeds and beautiful flowers. I believe he is trying to tell us that there is no magic formula for producing a good human being. A person's religious study or ritual observance will not automatically make them good; it will only make them good if they want it to. Ultimately, it's up to every individual Jew to decide whether to use the Torah as a source of technical, legal loopholes, or as an instrument for God-based goodness.