One who unintentionally mentions rain in the summer must go back and correct his mistake, since there is no praise in mentioning rain at that time. If he did not yet finish the berachah, he goes back to the beginning of it and says “Morid hatal,” as should be recited in the summer. If he already finished the berachah, he must start the Amidah again from the beginning in order to recite it properly, since the first three berachot are considered one unit (Shulchan Aruch 114:4).
One who mistakenly did not mention rain in the winter but instead mentioned dew, like we say in the summer, “Morid hatal,” need not repeat it since he recited some sort of praise relating to water. However, if he did not mention dew either, he must go back and repeat the entire Amidah, since he omitted such important words of praise (Shulchan Aruch 114:5).
One who incorrectly requests rain in the summer: since he made an inappropriate request in Birkat HaShanim, he must go back and correct it. Therefore, if he did not finish his Amidah yet, he returns to Birkat HaShanim, recites it properly, and continues in order from there until the end of the Amidah. If he already finished the Amidah, he recites the Amidah again properly from the beginning (Shulchan Aruch 117:3).
If, by mistake, one did not request rain in the winter, it depends how much of the Amidah he already recited. If he did not yet reach Birkat Shome’a Tefillah, he continues his prayer and when he arrives at Birkat Shome’a Tefillah, in which one is permitted to make any request, he asks for rain, thereby correcting his mistake. However, if he already passed Birkat Shome’a Tefillah, he missed the place in which he is able to correct himself and lost all the berachot that he recited after Birkat HaShanim. He must return to Birkat HaShanim, recite it in accordance with the halachah, and from then on continue to pray in the proper order. If he already finished the Amidah and was prepared to take three steps back, his prayer is considered insufficient since he did not request rain, and it must be repeated in the proper manner (Shulchan Aruch 117:4-5).