Praise be to Allah.
If a person omitted some words of the adhaan or iqaamah because he forgot them, if only a short time has passed then he should say what he omitted and complete it from that point. But if a long time has passed, then he should repeat the adhaan or iqaamah from the beginning.
If he repeats the adhaan or iqaamah in either case, there is nothing wrong with that.
Al-Nawawi (may Allah have mercy on him) said: If he omits some of the words of that [the adhaan], he should say what was omitted and what comes after it. But if he starts over, that is better. End quote.
The scholars of the Standing Committee for Issuing Faatwas were asked: What is the ruling if the muezzin forgets the words al-salaatu khayrun min al-nawm (prayer is better than sleep) in the adhaan of Fajr?
If the muezzin forgets part of the adhaan, then remembers whilst he is still saying the adhaan, he should say the words that he forgot and what comes after them of the words of the adhaan. If he does not remember until afterwards, then he should repeat the adhaan in full, if there is no other muezzin around him whose adhaan would fulfil the fard kifiaayah (communal obligation, i.e., of giving the call to prayer). End quote.
Fataawa al-Lajnah al-Daa’imah, 5/61
Shaykh Ibn Jibreen was asked: If the muezzin forgets the words al-salaatu khayrun min al-nawm (prayer is better than sleep) in the adhaan of Fajr, should he repeat the adhaan?
If he remembers straightaway, he should say al-salaatu khayrun min al-nawm (prayer is better than sleep). If he does not remember until after some time has passed, then it is waived, because it is Sunnah and there is no need to repeat the entire adhaan because of it. End quote from the Shaykh’s website.
The people of the mosque should have pointed out the muezzin’s mistake to him so that the words of the iqaamah would be correct. If they did not do that and the muezzin persisted in this mistake, then the prayer was valid and we hope that there is no sin on them because of that, because the iqaamah is Sunnah according to many scholars. Those who regard it is obligatory -- such as Imam Ahmad -- say that it is a communal obligation (fard kifaayah) and this obligation is discharged if there is another mosque in the same neighbourhood where the adhaan and iqaamah are said for prayer.
And Allah knows best.