Gemara

(Mishnah): If rain came after Nisan it is a curse - "Ha'Lo Ketzir Chitim ha'Yom..." (Shmuel wanted to show Benei Yisrael that their request for a king angered Hash-m. He prayed for rain to come in summer, and Hash-m brought rain.)

3a - Beraisa: Chachamim did not require one to mention dew and wind. If one wants to mention them he may.

R. Chanina: One is not obligated because they are never withheld.

3b - R. Chanina: Therefore, if in summer one mentioned wind he does not go back. If he mentioned rain he must go back;

In winter if one omitted (mention of) wind he does not go back. If he omitted rain he must go back. Even if he said '(Hash-m) removes wind and casts away dew', he does not go back.

Berachos 34a - Rav Huna: If one erred in one of the first three Berachos of Shemoneh Esre, he must return to the beginning.

Rishonim

Rif: In summer if one mentioned wind he does not go back. If he mentioned rain he must go back.

Yerushalmi - R. Ze'ira: If one mentioned dew in winter he does not go back; if he mentioned rain in the time of dew (summer) he must go back.

Question (Beraisa): Chachamim did not require one to mention dew and wind. If he wants to mention them he may.

Answer: One who prays and is Meikal is worse than one who does neither.

Ran (DH Yerushalmi): The questioner thought that R. Ze'ira requires one who mentioned rain in summer to go back because he (said like he used to say in winter and) did not mention dew. The Ramban explains that not mentioning either is no disgrace, but it is disgraceful to request what is not needed (rain) and neglect what is needed (dew). 'Meikal' does not denote a Klalah (curse); rather, it means 'disgraces' (the root is 'Kal'). Also, the Yerushalmi says that rain in summer is a curse only if it did not rain the entire winter. The Bavli says that that one who said 'He removes wind and casts away dew' does not go back. The Ramban says that the Rif brings the Yerushalmi because the Bavli agrees with it; mentioning rain but not dew is more disgraceful.

Rebuttal (Ran ibid.). It is difficult to say that mentioning rain but not dew is more disgraceful. 'Meikal' denotes a curse or Mekalkel (damages). The one who answered agrees that he goes back only if he mentioned rain but not dew, but not if he mentioned both, for usually rain is beneficial even in summer.

R. Yonah (on Rif Berachos 20a DH Mihu): If one mentioned rain in summer he goes back even in a region which needs rain in summer. In such a place one requests in Shome'a Tefilah. He may not change the text that Chachamim fixed.

Rambam (Hilchos Tefilah 10:8): In summer if one erred and mentioned rain he goes back to the beginning. If he did not mention dew he does not go back; for dew is never withheld.

Rosh (1:1): In summer if one mentioned wind he does not go back. If he mentioned rain he goes back to the beginning of the Berachah. If he finished the Berachah he goes back to the beginning of Tefilah, because the first three Berachos are like one.

The Yerushalmi says that if one does not know what he mentioned, within 30 days (of changing) we assume that he said like he was used to.

Question (Ran DH Tu): The Yerushalmi must discuss when it is now summer, for in winter even if one mentioned (dew) like he is used to, he does not go back. If it is still Nisan, why does he go back? Rain is never a curse then!

Answer (Ran ibid.): Since rain is usually a curse after we cease to mention it, Chachamim did not distinguish and said that one always goes back.

Rosh (Berachos 4:14): BaHaG says that one who prayed b'Tzibur would not repeat Shemoneh Esre due to a mistake. Rather, he is Yotzei by listening to the entire repetition of Shemoneh Esre. The Shali'ach Tzibur is Motzi even a Baki (one who knows how to pray). Even though R. Gamliel (Rosh Hashanah 34b) says that a Shali'ach Tzibur does not exempt people in the city, this refers to one who did not pray at all. He is Motzi one who prayed and erred.

Poskim

Shulchan Aruch (OC 114:4): In summer if one said Morid ha'Geshem he goes back to the beginning of the Berachah.

Mordechai (612): If one said Morid ha'Geshem in summer Machazirim Oso, i.e. we rebuke him so he will not do so again. It is unreasonable to say that he goes back to the beginning of the Berachah, for this does not help (his prayer is still improper)!

Beis Yosef (DH u'Mah she'Chosav v'Chozer): The Halachah does not follow the Mordechai. The Rambam says that he goes back to the beginning. This connotes that he always goes back to the beginning of Tefilah.

Question (Gra DH v'Chozer): Berachos 34a explicitly says that if one erred in one of the first three Berachos, he returns to the beginning of Tefilah. This is like the Rambam; the ruling of the Shulchan Aruch is difficult.

Chazon Ish (18:12): Since the first three Berachos are considered like one, anything said within them is considered part of Tefilah; returning to the beginning of the first Berachah is like returning to the middle of a Berachah! We must say that the Shulchan Aruch does not consider the first three Berachos to be like one regarding this. The Gra challenges this because there is no source for this distinction.

Mishnah Berurah (17): He goes back even if this is the day we cease mentioning rain.

Mishnah Berurah (19): B'Di'eved, if he went back to 'Rav Lehoshi'a' and finished the Berachah, this suffices.

Shulchan Aruch (ibid.): If he finished the Berachah he goes back to the beginning of Tefilah.

Mishnah Berurah (20): The Pri Megadim says that 'Baruch Atah Hashem' is considered finishing the Berachah. Others disagree. Rather, he should conclude "Lamdeni Chukecha" to avoid a Berachah l'Vatalah, and return to the beginning of the Berachah.

Kaf ha'Chayim (27): The Bach holds that as long as one has not started the next Berachah he need not return to the beginning. Since we are lenient about Safek Berachos, we rely on this.

Kaf ha'Chayim (29): Anyone who returns to the beginning because of a mistake b'Shogeg does not repeat 'Hashem Sefasai Tiftach'. One who returns because he deviated b'Mezid does repeat this.

Shulchan Aruch (ibid.): One must go back even in a region that needs rain in summer.

Mishnah Berurah (24): Even though one need not go back if he requested in such a place, it is improper to praise Hash-m by mentioning something that is a curse in other places.

Rema: The same applies if he mentioned rain and dew.

Shulchan Aruch (117:2): If an entire region needs rain in summer, and an individual erred and requested rain in Birkas ha'Shanim, he (Rema - may) pray again Tefilas Nedavah without requesting in Birkas ha'Shanim;

Kaf ha'Chayim (23): The Mechaber obligates one to go back.

Mishnah Berurah (10): If one realized his mistake in the middle, he finishes Shemoneh Esre and prays again Tefilas Nedavah.

Rema: He is not obligated to pray again at all.

Mishnah Berurah (11): In our lands, if there was no drought, one who requested rain between Pesach and Shavu'os must pray again Tefilas Nedavah.

Kaf ha'Chayim (26): It is best to intend that if the Halachah follows the Mechaber, his additional Shemoneh Esre is obligatory. It is good to have a Chidush intent.

Shulchan Aruch (117:3): If one requested rain in summer he must go back.

Beis Yosef (DH v'Im): This is worse than mentioning rain in summer, for which one must go back. One opinion says that one who mentioned dew and rain in summer does not go back, but all agree that one who requested dew and rain in summer goes back.

Mishnah Berurah (14): If he stepped back after Shemoneh Esre he goes back to the beginning of Tefilah. If not, he goes back to the beginning of Birkas ha'Shanim, even if he remembered in the middle of Birkas ha'Shanim.

Bi'ur Halachah (DH Im): If he went back to 'v'Ten Tal u'Matar' instead of the beginning of the Berachah, he was Yotzei b'Di'eved.

Mishnah Berurah (13): In a land which needs rain within 60 days after the Tekufah, if one requested rain then he must pray again Tefilas Nedavah.

Shulchan Aruch (124:10): If one made any mistake which requires him to repeat Shemoneh Esre, he should be Yotzei by listening to every word of the repetition as if he was praying himself.... Since he prayed but erred, the Shali'ach Tzibur is Motzi him even though he is Baki.

Sha'arei Teshuvah (114:3): If one erred regarding Meshiv ha'Ru'ach u'Morid ha'Geshem, he was not Yotzei the first three Berachos (they are like one), so it is as if he did not pray at all. If so, perhaps he cannot be Yotzei through the Shali'ach Tzibur.

Mishnah Berurah (124:39): The Shulchan Aruch connotes that one is Yotzei through the repetition no matter what mistake he made.

Mishnah Berurah (40,41): Nowadays it is better to pray again, for not everyone can hear every word from the Shali'ach Tzibur; perhaps he will miss a word that is Me'akev. If the Shali'ach Tzibur normally swallows words, or does not say all of Modim out loud, one must pray again himself.

Kaf ha'Chayim (54): One who is unsure whether or not he prayed may not be Shali'ach Tzibur, for the Shali'ach Tzibur must (Vadai) pray silently first. However, if one prayed Shemoneh Esre but must repeat it because of a mistake, this is considered that he prayed silently.

Kaf ha'Chayim (56): One may rely on being Yotzei through the Shali'ach Tzibur only if one knows that the Shali'ach Tzibur has Yir'as Shomayim and says every letter of the repetition audibly and says each word slowly by itself. Also, the listener must be able to listen without any stray thoughts.