In a simple case of the scribe mixing up the get and the receipt, we say that we are not sure that the wife in actuality received the Get and she is therefore not divorced. R. Eliezer makes a distinction between "immediately" and "later."
What difference should the time make? If the wife is "b'chezkat eishet ish" until we know for a fact that the husband gave her a get or died, why does the time factor make a difference? She remains an "eishet ish" until the get is given properly.
Chaim Sacknovitz, Jerusalem
Being that the scribe and others who were there to witness the divorce think they saw the man give the Get and not the receipt, she was considered divorced from then on, especially as it is probably a rare mistake for the scribe to give the man the receipt and the woman the Get. Rashi in the Mishnah (based on Rav Ada bar Ahava on 80b) explains that if this was only revealed after a while, we suspect that the divorced couple conspired to switch documents after she married a second husband, in order to help her get out of the second marriage. The fact that witnesses saw that she became divorced (although they cannot testify for certain that the document was a Get) combined with a strong suspicion of conspiracy indicate that she stays married to her second husband.
All the best,
Yaakov Montrose