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Our Mishnah relates that on one occasion witnesses did not arrive to testify about the new moon until after the time of Minchah on Rosh Hashanah. As a result, the Leviyim did not recite the correct Shir when the afternoon Korban Tamid was offered. Because of that "Kilkul" the Rabanan instituted that Beis Din may never accept witnesses who come to testify about the new moon after the time of Minchah.
Why does the Mishnah say that the "Kilkul" was that the Leviyim recited the wrong Shir? Since the witnesses did not come until after the afternoon Korban Tamid was offered, there was a much more serious "Kilkul": the Korban Musaf of Rosh Hashanah could not be offered.
The afternoon Korban Tamid must be the last Korban of the day (Pesachim 58b), and since they already brought the Korban Tamid they could not bring the Korban Musaf. Consequently, not only did the late arrival of the witnesses result in the wrong Shir being recited, but it resulted in the inability to offer the entire Musaf offering of Rosh Hashanah. Why does the Mishnah not mention this "Kilkul"?
The RAMBAM (Hilchos Kidush ha'Chodesh 3:5) explains that the "Kilkul" indeed was that they did not offer the Korban Musaf. He makes no mention of the Shir.
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