What is the meaning of "va'Yitu Acharei ha'Batza"?
Radak: Their hearts passionately desired wealth. Judges should be "Sonei Batza" (Shemos 18:21), who are satisfied with their monetary status, and do not pursue wealth! Batza is not theft and bribery, for the verse already said "Anshei Emes."
Radak citing Targum Yonasan: They went after false [ways to obtain] money.
What was their sin "va'Yitu Acharei ha'Batza [va'Yikchu Shochad]"?
Rashi (like R. Shmuel bar Nachmani, Shabbos 56a): They did not sin, just they stayed in their cities and judged, in order to benefit their Chazanim and scribes.
Radak (2, like R. Meir Shabbos 56a): They explicitly requested Ma'aser Rishon (and people would not refuse them. This hurt other Leviyim).
R. Yehudah (Shabbos 56a): /They gave merchandise to people for business. The latter would return the profit [and Bnei Shmuel would favor these people in judgment].
R. Akiva (Shabbos 56a): They took by force more Ma'aser than they were entitled to.
Radak (2, like R. Yosi Shabbos 56a): They took by force Matanos (Ma'aser Rishon. Alternatively, the foreleg, jaw and stomach of Chulin animals, which should be given to a Kohen.)
Malbim: One sin led to another. They did not go in Shmuel's way to go around to judge, and later they pursued Batza (like Chazal said - refer to 8:3:2:1-5), and later they took bribes and tilted judgment.
QUESTIONS ON RASHI
Rashi writes that "they pursued Batza" means that they stayed in their cities. Is a judge obligated to go around to judge?
Bach (CM 9:8): Yes! The Tur brings so from the Ramban (Hilchos Sanhedrin 23:3). 1 However, nowadays he need not, for there are few Yisraelim in each city, and the roads are dangerous.
Me'iri (56a): One is not liable for not conducting with Midas Chasidus. However, if one's fathers were famous for such a Midah, and he comes to fill his father's place, for him it is considered average, and if he does not fulfill it, he should be punished. Rav Elyashiv (56a) - presumably Shmuel trained them according to his Midah. They are liable for not conducting like their father.
Perhaps even according to the opinion that Devorah was truly a judge, it is not proper for a woman to travel so much - "Kol Kevudah Vas Melech Penimah" (Tehilim 45:14). (PF) Pesach Einayim (56a) - the Gemara implies that it was evil because they intended to benefit their Chazanim and scribes, but if one stays stationary to avoid toil, it is not evil, unlike the Bach.