R. Zeira told his assistant to have Kavanah when blowing Shofar for him.

We see that he holds that the one blowing must have Kavanah

Question: We find that if someone was passing by a Shul and heard the Shofar or Megillah, then he is Yotzei only if he had Kavanah - but in any case, the one blowing certainly didn't have Kavanah for him!?

Answer: The one blowing is a Shali'ach Tzibur who has Kavanah for everyone.

Question: We find that both the Shofar-blower and the listener must have Kavanah. The implication is that if the listener had Kavanah but not the blower, he is not Yotzei - which must refer to the blower not having himself in mind and not being Yotzei (just like the other case mentioned there, namely, of the listener, who did also not have Kavanah that he himself should be Yotzei). But if he did have himself in mind, they are Yotzei even though he had nobody else in mind!

Answer: It is a Machlokes Tana'im:

(Tana Kama): The one blowing does not need any specific Kavanah for anyone.

(R. Yosi): That is only true for a Shali'ach Tzibur, otherwise both blower and listener must have Kavanah.

The Pasuk says that the Bnei Yisrael were victorious when Moshe's hands were raised, as it signified that their hearts were directed Heavenwards.

Similarly, the copper snake had no innate healing powers, but it caused people to direct their hearts Heavenwards.

A deaf-mute, fool or minor cannot blow Shofar for the rest of us.

The principle is that anyone not obligated in something cannot perform other's obligations in it.

A Beraisa discusses the obligations for Shofar:

Everyone is obligated in Shofar, including Kohanim, Levi'im, Yisraelim, converts, freed servants, Tumtum, Androgenus, and one is half enslaved and half free.

A Tumtum cannot be Motzi either another Tumtum or other people.

An Androgenus can be Motzi another Androgenus but nobody else.

Someone who is half enslaved and half free cannot be Motzi either a similar person or anyone else.

Question: Why do we need to be told that Kohanim, Levi'im and Yisraelim need to hear Shofar?

Suggested answer: We might have thought that Kohanim are exempt, as it is called a "day" of Shofar, and their obligation is year-round with the trumpets of the Olos.

Objection: Trumpets are a different matter to Shofros!?

Replacement answer: We might have thought that Kohanim are exempt for a different reason:

The Mishnah said that Rosh Hashanah and Yovel are the same regarding Shofar.

We might have taken this to mean that those who are exempt from Yovel are exempt from Shofar.

Kohanim are exempt from Yovel in that they can sell their property at all times and redeem it.

(R. Huna): Although someone who is half enslaved and half free cannot be Motzi either a similar person or anyone else, he can be Motzi himself.

Question (R. Nachman): Just as his slave half cannot be Motzi someone else's free half, it also cannot be Motzi his own free half!

Therefore, he cannot be Motzi himself either.

A Beraisa confirms this.

Although a person has been Yotzei a Berachah for himself, he can still be Motzi others, except for Berachos on food.

Question (Rava): Can a person be Motzi others with the Berachah on matzah or the wine of Kidush after he has already been Yotzei?

Do we say that this Berachah is part of the obligation or not?

Answer (R. Ashi): R. Papi used to make Kidush for us and then for his worker.

A person should not make a Berachah for his guests if he is not himself eating.

But he can do so for his children and household in order to educate them.

A person may read Hallel and Megillah to be Motzi others even though he has already been Yotzei.

If Rosh Hashanah fell on Shabbos, they would blow Shofar only in the Beis ha'Mikdash.

After the Destruction, R. Yochanan ben Zakai decreed that it should be blown in every town with a Beis Din.

R. Elazar said that this decree was only for Yavneh, but others disagreed.

With Yerushalayim, all nearby towns could also blow Shofar on Shabbos, whereas with Yavneh no other towns could do so.

Question: How do we know that Shofar must not be blown on Shabbos?

Answer: Although one Pasuk says that it should be a day of Teru'ah, another says that it should be merely a remembrance for Teru'ah, which must be referring to where it fell on Shabbos.

Question (Rava): If it is forbidden d'Oraisa, how could they blow it on Shabbos in the Beis ha'Mikdash?

Question #2: It's not a Melachah anyway; as with removing the bread from the oven, it is a Chochmah.

Replacement answer (Rava): It is permitted d'Oraisa; the Rabanan prohibited it, in accordance with Rabah:

(Rabah): Everyone is obligated to blow Shofar, but not everyone is competent to do so.

There is therefore a concern that a person might carry it on Shabbos to an expert for instruction.

It is for this reason that the Rabanan forbade Lulav and Megilah on Shabbos.

Once, when Rosh Hashanah fell on Shabbos, all the towns went to Yavneh to hear the Shofar blown.

The Bnei Beseirah asked R. Yochanan ben Zakai to judge whether the decree of not blowing the Shofar should be applied.

He told them to blow the Shofar first, and afterwards he said that it was too late to judge it.

Question: In the Mishnah, those who said that the Shofar was not only blown on Shabbos in Yavneh but also in every town with a Beis Din are saying the same thing as the Tana Kama!?

Answer: The difference is with a temporary Beis Din, which only the Tana Kama would permit to blow a Shofar on Shabbos.