One would not expect the laws of divorce to be affected by one's location. Thus it comes as a bit of a surprise to open masechet Gittin and read "one who brings a get from across the sea must say 'in front of me it was written and in front of me it was signed" (Gittin 2a). Such a declaration is absent when the get is being written and delivered in Israel. Why the difference?
Rabba, living in Bavel at the turn of the 4th century claims because "they are not expert [in the need] of [proper] intent." One of the key requirements of a get is that it be written lishma, specifically for the sake of the couple divorcing. Yet this law was not sufficiently well known outside the land of Israel. The rabbis thus required that an agent bringing a get must declare that it was written and signed before him indicating it was done with proper intent. As to why the agent need not say "it was written before me lishma and it was signed before me lishma" the Gemara explains that such a long declaration might be too much to ask someone to remember and say properly. One must keep ones' instructions simple and clear, four words are manageable but six is pushing it.
Rava finds this approach unconvincing, to say the least. Haikar chaser min hasefer, the main part is missing from the book! If it with lishma that we are concerned then that is the last thing one should leave out. That the Sages did not require mention of lishma indicates that this law was well known even outside the land of Israel. Rather the declaration of the agent is needed due to the difficulty of travel in the ancient world. The rabbis feared that should the husband claim he never authorized the writing of the get - maybe divorce was not the wisest decision to make after all - it would be impossible to verify that the signatories on the get are legitimate. Lacking copies of the signatories in Israel the only way to verify them is to send people back "across the sea" and that is just not realistic. Even when possible it would take much too long leaving the woman an agunah in the interim. The declaration "before me it was written and before me it was signed" serves as the authentication of the signatories and any claim of forgery is hence force rejected.
It is this fear of having a woman become an agunah that motivated the rabbis to allow just one agent testifying that the get was properly executed and the signatories valid. By the normal rules of jurisprudence we should require two witnesses to ensure the validity of the get. Our Sages sensitive to the tragedy of the agunah relaxed the rules of testimony, meshoom agunah akeelu bo rabbanan.
As the need for declaration of "in front of me it was written and in front of me it was signed" is not intrinsic to the get itself it is subject to change as condition change. "It was said: Bavel, Rav says it is like the land of Israel for the purpose of Gittin, and Shmuel says it is like [all other places] outside the land" (Gittin 6a).
It was Rav who established the great academy in the city of Sura and can be credited with turning Bavel into the preeminent Torah center it was to occupy for some 800 years. Due to his great influence there was no longer any fear that a court would issue a getnot written lishma. Yet while Rav's influence eliminated the need for a witness to testify a get was written lishma such knowledge does little to eliminate the problem of difficulty of witnesses travelling to verify the signatories to the get. As the Gemara explains Rabba was concerned both about lishma and authenticating the signatories to the get.
The Gemara explains that the establishment of Yeshivot in Bavel not only obviated the fear of a get not being written lishma it also obviated the need for witnesses to authenticate the get. With so many centers of learning one can be certain that students and teachers would be travelling back and forth from one yeshiva to another, something we do know from many Talmudic sources, making it easy to verify documents. On the other hand Shmuel felt that one could not rely on students to verify signatures. They are (or should be) so exclusively involved in their studies that they are oblivious to their surroundings and are unable to identify the signatures of others. Apparently Rav and Shmuel had different understandings of how yeshiva students interacted with the world around them.
 As to how the rabbis can change the law the Gemara explains that in reality most were aware of the law that a get had to be written lishma and the requirement for saying "before me it was written..." is only rabbinic in nature. As a rabbinic law the rabbis are well within their power to relax or even ignore this law. Similarly authentication of witnesses is also only a rabbinic law. At the same time see here for a discussion of how the rabbis could override the biblical law allowing a women to remarry based on the testimony of only one witness.
 I find it somewhat ironic that Shmuel himself said, "the paths of heaven are as clear to me as the pathways of Nehardea" (Brachot 58b).