All right, I'll put up some notes on Gittin, but most of these are technical and will only be of interest to people who are learning Gittin right now (if that!).
Why does Gittin begin with a proxy delivering a get? Perhaps because the hand-to-hand delivery is one of the few elements spelled out biblically (the Torah explicitly mentions the husband giving the get to his wife), and so the gemara begins with that which is חביב, beloved, to the sages, that which is extrapolated and clarified rabbinically. A similar approach is used in the beginning of Shabbos (Tosafot on starting with Hotzaah) and the beginning of Yevamot (the gemara on the order of the 15 cases in the first mishnah there).
See Tosafot ממדינת on why we talk about “islands in the sea” instead of the generic “חוץ לארץ outside of Israel.”
See the first Tosafot לפי on why we single out this one law - the לשמה requirement - as a law with which Jews living in galut were not familiar.
The issue of trustworthiness here is very important. It isn’t that we don’t trust those batei din, it’s that we think they don’t know everything they need to know. This comes up in all sorts of areas, such as kashrut - we may trust the sincerity of a person, but we also need to determine his level of knowledge.
Tosafot חד explains that we are not only concerned that the husband might disqualify the Get; we are also concerned that he might cause general trouble.
Rashi ואין בו אלא עד אחד sides with Shemuel from a debate on Gittin 86a-b; this is problematic, given that we side with Rav there! Also, see Rashi there ואם.
What is Rabbah bar bar Chanah adding with his Bei Kubi-Pumbedita example? Perhaps it is just an example for Babylonians who had not seen the Israeli examples.
About ¾ of the way down the page: If there are many courts around, why will people in different cities know each other’s signatures? Just the opposite - everyone will go to their own courts!
Nachlat Moshe suggests that the courts themselves may have networked, through agents who traveled to the different courts. Also, בתי דינין דביעי may not be as Rashi took it, but may mean one central court, to which everyone went.
Rabbi Shimon bar Abba’s hypothetical invisible ally doesn’t solve the problem - we should still be concerned lest the situation worsen! (Unless we don’t make the decree because having two deliverers is unusual?)
I thank Rabbi Ian Bailey for reminding me that Bar Hedya, who is a get-deliverer trainee here, was also the money-hungry dream-interpreter in Berachot 56.
See Tosafot מכי on what changed when Rav arrived in Bavel.
Very interesting: R’ Ila’i raised a problem with R’ Yishmael’s position, out of ignorance, and R’ Yishmael did not embarrass him by correcting him. Rather, he simply said, “Leave it be” and allowed R’ Ila’i to think him mistaken.
See Tosafot זבוב on how the fly/hair explanations fit the pasuk.
The apparently pluralistic idea here of אלו ואלו דברי אלקים חיים, “These and these are the words of the living Gd” (or “These and these are the living words of Gd”), is very important. Although the story under discussion is a historical event which must have happened one way or another, Gd will value each interpretation simply because it was stated by a serious student who was trying to understand the story. Thus Gd will honor each of those statements as statements of Torah.
See Tosafot שלש.