Gittin, Chapter 8, Mishnah 8. This mishnah divides into two parts: the first deals with another case of an error that occurred with a get, and with the penalties listed in the previous mishnah, which apply here as well.
The Case: The Get and the Receipt Were Switched:
The mishnah opens: "Kasav sofer get la'ish v'shovar la'ishah" - the scribe writes the get for the husband, since he is the one who hands the get to the woman and he is the one who is supposed to hold it until the moment of delivery; and at the same time he writes a receipt for the woman.
What is a shovar? Upon divorce, the woman is going to collect her kesubah. To show that she received payment of the kesubah, she hands the husband a receipt, and that is called a 'shovar' - from the word for breaking, since it breaks the force of the kesubah document and serves as proof for the husband that he paid. Therefore it is the way of a scribe who writes the divorce documents to hand the get to the husband and the receipt to the woman, so that she can give it to him when she receives her kesubah.
Here, however, "ta'ah v'nasan get la'ishah v'shovar la'ish" - the scribe mixed them up and handed the get to the woman and the receipt to the man, "v'nasnu zeh la'zeh" - and they handed the documents to one another: the man thinks he is holding a get, and the woman thinks she is holding a receipt, when in truth each one was holding the opposite.
It turns out that the man never divorced his wife at all, since he handed her a document that has no bearing on divorce; it is relevant to her, but on the monetary level alone. After some time the matter comes to light: "ha'get yotzei mi'yad ha'ish v'shovar mi'yad ha'ishah" - the man looks and finds a get in his hand instead of a receipt, and the woman searches for her get and finds in her hand a receipt she received from the man. From here it is clear that an error occurred.
Therefore "teitzei mi'zeh u'mi'zeh" - she must leave both the second husband whom she married on the strength of this get, and her first husband. And all those measures and penalties listed in the previous mishnah apply here as well.
The Opinion of Rabbi Eliezer:
Rabbi Eliezer disagrees and holds that the matter is not so simple, and he distinguishes between two situations:
"Im l'alter yatza ein zeh get" - if immediately after the delivery the documents were checked and the error was discovered, this is not a valid get, as explained.
"Im l'achar zman yatza harei zeh get" - if time passed, and only then was it discovered that the woman produces a receipt and the man produces a get, the get is valid and the divorce took effect.
And why? "Lo kol heimenu l'abed es zechus ha'sheni" - the first husband does not have the power to nullify the right of the second husband, who married her on the strength of the get, and now, some time afterward, the first produces a get that was not supposed to be in his possession.
What stands behind this? The concern is that the first husband and the woman decided to return to one another, because she is not happy with the second husband. In truth the documents were delivered properly - he gave her the get and she gave him the receipt - only that afterward they switched the documents between them, and now she produces the get and he produces the receipt, and they pretend that the documents were delivered the wrong way around. Therefore, once time has passed, the first husband does not have the power to uproot the second marriage, since it is possible that the switch was made after the fact and the get was valid from the outset.
He Wrote a Get to Divorce His Wife and Then Changed His Mind:
From here the mishnah moves to an entirely different case: a man who wrote a get for his wife and afterward changed his mind and decided not to hand it to her.
Beis Shammai say: "Pesalah min ha'kehunah" - even though the get was never handed to her, the very writing of the get for her sake disqualifies her from marrying a kohen. She is not really a divorcee, but the matter resembles divorce closely enough for the Sages to decree and treat her as a divorcee with regard to marrying a kohen.
And Beis Hillel say - the exact opposite: even if he actually gave her the get, and gave it on a condition that was not fulfilled, she is not disqualified from the kehunah.
On the face of it this case very much resembles a valid get, since the get was even placed in her hand. Nevertheless she is not divorced, since everyone agrees that the condition upon which the get was given was not fulfilled. One might have thought that the matter is close enough to a get, since everyone sees the delivery, and therefore the Sages would decree and treat her as a divorcee who may not marry a kohen. Along come Beis Hillel and say: since this is not a valid get, she is not a divorcee at all, and she is permitted to marry a kohen.
In summary: in the first part of the mishnah we learned about a scribe who erred and switched the get with the receipt, and as a result the man and the woman handed each other the wrong documents - that there is no divorce here, and she must leave both men with all the penalties listed in the previous mishnah. Rabbi Eliezer distinguished between a case where the error was discovered immediately, in which case it is not a get, and a case where it was discovered after time had passed, in which case the get is valid, out of concern that they switched the documents after the fact, and because the first husband does not have the power to destroy the right of the second. In the second part we examined the dispute between Beis Shammai and Beis Hillel regarding one who writes a get and then changes his mind: according to Beis Shammai she is disqualified from the kehunah, and according to Beis Hillel even a get given on a condition that was not fulfilled does not disqualify her.