Sanhedrin 23: Judge Selection
Chapter 3! Returning to the courts for monetary matters of 3 judges, with more details and procedure too. The new mishnah addresses choosing judges for the court and whether a litigant can disqualify a judge if he is halakhically fit to be a judge (machloket, of course). The Gemara delves into the question of selecting and disqualifying a judge -- applying it to a very specific case with a choice of a secular judge. Plus, the role of a judge's expertise in whether he can be disqualified. Note that the litigants' appointment of judges presumes that they are choosing people who are fit to be judges to begin with.