1. מצוה למימני יומי ומצוה למימני שבועי
Abaye said regarding sefiras ha’Omer: מצוה למימני יומי ומצוה למימני שבועי – it is a mitzvah to count days, and it is a mitzvah to count weeks. The Rabbonon of Rav Ashi’s yeshivah counted the days and counted the weeks. However, Ameimar only counted the days, but did not count the weeks. He explained that after the חורבן of the Beis Hamikdash, when the עומר is no longer offered, זכר למקדש הוא – [the mitzvah of ספירת העומר] is only kept as a remembrance for the Mikdash, and counting just the days suffices.
2. Machlokes how the barley for the עומר was toasted
In the next Mishnah, Rebbe Meir says that after the harvested barley was put into baskets, it was brought into the עזרה, והיו מהבהבין אותו באור – and they toasted it over the fire, כדי לקיים בו מצות קלי – in order to fulfill the mitzvah of toasting. But the Chochomim say the barley was first threshed, which was done with soft reeds and stems so the kernels would not be crushed. The kernels were then placed in an אבוב – copper pipe to be toasted, which was מנוקב – perforated, כדי שיהא האור שולט בכולו – so that the fire would have power over all of it. It was then spread out in the עזרה, and the wind would blow on it. It was then ground in a bean mill, and an עשרון of fine flour was obtained after sifting it through thirteen sieves. In a Baraisa, Rebbe Meir explains that "קלוי באש" – toasted in a fire teaches שהיו ישראל מהבהבין אותו באש – that Yisroel would toast it over fire. But the Chochomim say: אין אור לשון קלי – directly toasting over a fire is not "קלי"; אלא דבר אחר – rather, it means toasting with something else in between. Alternatively, אין לשון קלי אלא דבר קליל – the term "קלי" only implies something shiny, i.e., a shiny copper pipe for toasting.
3. מירוח הקדש פוטר, machlokes if שירים of עומר is subject to מעשר
The Mishnah concluded: והשאר נפדה ונאכל לכל אדם – the remainder of the barley flour (which was not used for the עומר) is redeemed and may be eaten by anyone, and it is subject to the חלה obligation, but exempt from maaser, since it was owned by hekdesh during מירוח – smoothing the grain piles (the completion of the processing). Rebbe Akiva says it is subject to maaser as well. Rav Kahana explained that Rebbe Akiva holds that מירוח הקדש – smoothing of grain while it belongs to hekdesh does not exempt it from maaser. However, the Gemara proves that Rebbe Akiva agrees that מירוח הקדש generally exempts from maaser, and Rebbe Yochanan explains Rebbe Akiva’s opinion: תלמוד ערוך הוא בפיו של ר' עקיבא – it is an established teaching in Rebbe Akiva’s mouth שלא ניתנו מעות אלא לצורך להן – that [hekdesh] money is only given for what they are needed for, i.e., the עשרון of flour. The rest of the three סאה was never hekdesh and is not exempt from maaser. (Tosafos discusses if it requires redemption).