Edut Meyuchedet

At the end of the mishna, the Tanna cites an alternate interpretation of על פי שנים עדים - namely: that the Sanhedrin should not hear the testimony of the edim via a תורגמן- translator.  The words על פי are now understood as "directly from the mouths of the edim" - to the court.

In summary, we have a number of possible explanations of the expression:
a) At its simplest level, this is an expression indicating that the testimony regarding the case must be uttered to the court by two witnesses.
b) R. Yosi: the פה referred to here is the mouth of the witnesses as those who must warn the accusued of the ramifications of his actions.  According to this view, the expression in relating to a stage PRIOR to testimony in Bet Din, at the event itself.  The edim must utter the warning, and not a third party
c) דבר אחר - last view in the mishna: edim must utter the testimony directly to the court, and not via a translator.

The Gemara begins with a related, but not identical issue as that raised in the body of the mishna: עדות מיוחת: simultaneous, but not joint, viewing of the murder.  Instead of the mishna's case - in which there was a full "כת" of edim in each window, viewing the event, there was only one עד in each window, but neither one saw each other.  Rav Zutrah bar Tuvyah's goal is to prove that such an 'edut' is invalid.  His source is our pasuk על פי שנים עדים; at the very end of the pasuk, the Torah reads לא יומת על פי עד אחד.  Rav Zutrah shows us his logic - by first discounting the simple pshat - ie that the Torah is invalidating the testimony of a single witness in capital cases.  How so? That halacha is already implied in the רישא,  opening of the pasuk: after all, if two edim are required, one is insufficient!  Therefore, the end of the pasuk refers to a total of two witnesses, but who viewed the event independent of one another; the pasuk relates to the number of edim in the context of the viewing of the event, not the actual testimony....Such an edut is invalid.

The gemeara confirms Rav Zutrah's halacha by citing a supporting baraita that ends with the following logic :  not only two simultaneous viewings are not "mitztaref" (joined) to form one edut, but even two people who viewed an event from the same window, one after the other, are not "mitztaref" to form one edut.

Rav Pappa raises an objection to Abaye: This is not a bigger "chiddush" - but it flows as a קל וחומר of the first halacha: In the first case, each witness saw the entire act and the edut was still not formed - how much moreso when each witness each saw half the act.........