Moses' seat was a symbolic expression of teaching the Pentateuch. Furthermore, it pertained more to civil law than issuing religious dogma. Moses was judge; the priesthood constituted a theocracy. These Jewish leaders did not continually make up new laws, but rather upheld the laws that God had originally given to His people through Moses. They could teach only to the extent of what the Law said.
Roman Catholics assume without proof that there exists a logical connection between Moses' seat and their chain of Papal successors. They commit eisegesis by applying Matthew 23:1-2 to their church hierarchy. The New Testament says nothing concerning a chair of Peter, let alone apostolic successors. Christ says nothing in Matthew 23:1-2 about adherence to extra-biblical traditions. There is no evidence for a tradition of successors from Moses' seat. Neither is there any evidence existing that the Jewish people attributed infallibility to their leaders. In fact, we know from Scripture that the scribes and Pharisees promulgated doctrinal error. They were even called by Jesus "blind guides" and accused of "teaching as doctrines the commandments of men" (Matthew 15:1-9; 23:16).
Whatever teaching from the writings of Moses and the Prophets that the scribes and Pharisees had taught, Christ instructed the people to obey. Their teachings in that regard were authoritative. However, He told them to not emulate their moral and doctrinal errors (Matthew 23:3). These men made themselves appear extremely pious and zealous in their daily religious practices before others, but God knew that their hearts were far from Him. He knew that the scribes and Pharisees were only seeking flattery from the public. Their worship of God was only outward, which is something that He absolutely detests. If anything at all, we should take this passage of Scripture as a warning against pride.