In the list of "beis din yafeh" why is "achar chachamim lelishkas hagazis" last; should be first?
I assume that the basis for your question is both that the Sanhedrin sat in Lashkas ha'Gazis well before the times of the Batei Dinim of the Chachamim mentioned in the Gemara, and the the Sanhedrin of the Lishkas ha'Gazis were clearly a more competent authority than any of the Batei Dinim mentioned in our Gemara. Excellent question (although I did not find any Acharon who addresses it directly).
An answer may be suggested if we first consider why the Gemara had to learn from "Tzedek Tzedek" that one should go to the Sanhedrin in Lishkas ha'Gazis; the verse says openly "When you have a doubt as to the Halachah, go to the place which Hash-m will choose..." (Devarim 17:8). Apparently, the Gemara means that even when a person can go to a lower Halachic authority for a ruling (i.e. the lower level court was not stymied), it is best to go straight to the top, to the Lishkas ha'Gazis.
The Gemara, then, is teaching two different pieces of advice (perhaps the two are learnt from the two "Tzedek"s of the verse):
1) A person should not go to an impromptu court, but to the established court of the region ("Achar Chachamim -- l'Yeshivah!"). This teaching is accompanied by a number of examples which describe the more famous courts of each region in Israel.
2) A person should not even go to an established court if he can go to the Great Sanhedrin of the Lishkas ha'Gazis ("Achar Chachamim -- l'Lishkas ha'Gazis!"). This is obviously a much greater Chidush, since even though an established court is available and we are advising to go to another court, the Sanhedrin.
If so, the Beraisa's teachings are arranged in order of "Lo Zu Af Zu": Not only should one avoid non-established courts, one should even avoid regional established courts if it is possible to go to the Great Sanhedrin in the Lishkas ha'Gazis, whose authority surpasses that of any other court.