"disputes": These are (questions concerning) the sotah's draught, the breaking of the heifer's neck, and the cleansing of the leper.
"in your gates": These are (questions concerning) leket, shikchah, and peah.
"and go up to the place, etc.": From here it was derived that there were three batei-din there: one at the entrance to the Temple mount, one at the entrance of the azarah (the Temple court), and one in the chamber of hewn stone (the seat of the great Sanhedrin).
They (the dissenting sage and his colleagues in the local court) come to the court at the entrance of the Temple mount, and he (the dissenting sage) says to them (the members of that court): Thus have I expounded, and thus have my colleagues expounded. If they (the latter) have heard (the ruling in that matter), they tell them; if not they (the dissenter and his colleagues) come to the one at the entrance of the azarah), and he (the dissenter) says (to them): Thus did I expound and thus did my colleagues expound; thus did I teach and thus did my colleagues teach. If they have heard, they tell them; if not, they all come to the great beth-din (the Sanhedrin) in the chamber of hewn stone, whence Torah goes forth to all of Israel, as it is written (Devarim, Ibid.) "to the place which the L-rd your G-d chooses."