Commentary for Sanhedrin 4:2
דִּינֵי הַטֻּמְאוֹת וְהַטָּהֳרוֹת מַתְחִילִין מִן הַגָּדוֹל, דִּינֵי נְפָשׁוֹת מַתְחִילִין מִן הַצָּד. הַכֹּל כְּשֵׁרִין לָדוּן דִּינֵי מָמוֹנוֹת וְאֵין הַכֹּל כְּשֵׁרִין לָדוּן דִּינֵי נְפָשׁוֹת, אֶלָּא כֹהֲנִים, לְוִיִּם, וְיִשְׂרְאֵלִים הַמַּשִּׂיאִין לַכְּהֻנָּה:
Cases of (ritual) uncleanliness and cleanliness begin from the senior (judge). Capital cases begin from the side [i.e., from those lesser in wisdom, who sat at the side, it being written (Exodus 23:2): "Do not answer upon riv (written "rav") to deviate." That is, do not answer after the elect one in beth-din, to deviate from his words. For this reason, his words are heard only at the end.] All are kasher to adjudicate monetary litigations, [even a proselyte, if his mother were a Jewess. And a mamzer, too, is kasher to adjudicate monetary litigations.] But not all are kasher to adjudicate capital cases, but only Cohanim, Levites, and Israelites who can marry into the priesthood, [it being written (Exodus 18:22): "And let them lighten your burden and bear with you (Moses)" — they must be like you. Just as Moses our teacher was "pedigreed," so beth-din must be pedigreed.]
Bartenura on Mishnah Sanhedrin
English Explanation of Mishnah Sanhedrin
All are qualified to try non-capital cases, but not all are qualified to try capital cases, only priests, levites and Israelites that may give [their daughters] in marriage to priests.
Mishnah two contains more information regarding the differences between capital and non-capital cases.
This mishnah contains an additional two differences between non-capital cases and capital cases. (We learned of eight differences in mishnah one.)
In all types of non-capital cases the eldest judge may state his opinion first, but in capital cases the decision stating process begins from the side of the room, where the younger members of the court would sit. This is to prevent the youngest judge from being unduly influenced by the opinion of the eldest judge.
A person of any lineage may judge non-capital cases, even mamzerim (those born of illicit unions) and even converts. However, only those who can marry their daughters to priests, meaning priests, levites and Israelites can judge capital cases. This law certainly reflects the import that the Rabbinic society ascribed to familial relations.