Even R. Eliezer holds no signatures are required for a Get. If the signatures are Nochrim and their names are not necessarily Nochri-ish names the Get is Pasul. (1)
R. Eliezer Bar Yosi says that R. Akiva and the Chachamim agree that Shetaros and Gitin that are written and signed in a Nochri court are Kosher.
The argument between R. Akiva and the Chachamim is with respect to Shetaros that are written and signed by Hedyotos. (2)
R. Shimon Ben Gamliel holds that Gitin that are signed by Nochrim are only Kosher in a place that the Jews are not allowed to sign. (3)
Ravina says that the holder of a Shtar that was written and signed by Persians may only collect from Bnei Chorin, not from Mishu'abadim. (4)
A Shtar must be written on parchment that cannot be erased.
The last line of a Shtar must consist of a summary of the Shtar.
A Get that comes from Eretz Yisrael and the signatures on the Get are Nochrim the Get is Pasul if the names are sometimes used by Jews. (5)
A Get that comes from Medinas ha'Yam even if the signatures are Nochri names the Get is Kosher because most of Klal Yisrael in Chutz la'Aretz have Nochri names.
R. Meir says that if someone gives a Shali'ach a Get or Shtar Shichrur to give to his wife or servant he may retract before it reaches their hands.
The Chachamim hold that he may retract the Get and not the Shichrur because the Get is a Chov and the Shichrur is a Zechus. (6)
A person who grabs someone's property for his Ba'al Chov is not Koneh if it is a Chov for another person. (7)
R. Eliezer says that if someone collects Pe'ah for his friend who is an Ani he is Zocheh, but the Chachamim hold that he must give it to the first Ani that he finds.
A BIT MORE
1. Because of the concern that the Get will be given to the woman in front of the signatories and since they are Nochrim the Get will be Pasul. However if the names on the signatures are obvious Nochri names the Get is Kosher according to R. Eliezer since there is no concern that the Get will be given in front of them.
2. R. Akiva holds that they are Kosher and the Chachamim hold that they are Pasul.
3. Since they are not allowed to sign there is no concern that we will rely on the signatories to witness the Mesirah of the Get.
4. Since the signatures are from Nochrim the Shtar does not have a Kol and therefore we do not allow him to collect from Mishu'abadim.
5. The Get is Pasul even if it is given over in front of Eidei Mesirah according to R. Eliezer who holds that no signatures are required for a Get because it is Mezuyaf mi'Tocho since the signatories may be Nochrim. However if the names are used only by Nochrim the Get is Kosher according to R. Eliezer since we will know not to rely on the Edim of the Get and we will not use them for the Eidei Mesirah.
6. The Get is a Chov because the husband is obligated to give Mezonos to his wife while a Shichrur is a Zechus because a person is not obligated to give Mezonos to his servant.
7. If Reuven owes money to both Shimon and Levi, if someone grabs the property of Reuven for Shimon it is a Chov for Levi and therefore he is not Koneh.
Ravina wanted to be Machshir a Shtar that was written b'Kenufyasa d'Armai (a gathering of Arma'im) and Rafram objected with the logic that the Mishnah says that only Shetaros that are written in a Nochri court are Kosher and not a Shtar that is written by Hedyotos. The Chasam Sofer explains that although a Kenufyasa d'Armai is not regarded as a court, however it is better than Hedyotos and for that reason Ravina thought that it is Kosher. However Rafram held that since the Mishnah says that the Shtar must be written in court any Shtar that is not written in court is not Kosher even in a Kenufyasa d'Armai even though it is better than Hedyotos.
If someone writes a Shtar Shichrur for his servant and gives it to a Shali'ach and tells him to be Zocheh in this Get for my servant the servant goes free immediately even though he has not yet received the Get, because one can be Zocheh for a person even if he is not present. However if he says to the Shali'ach give this Get to my servant he cannot retract, but the servant does not go free until he receives the Get (Rambam Hilchos Avadim 6:1)