If the chazan (cantor) makes an error in his personal tefilat lachash (silent prayer), an error that would normally require an individual to go back and repeat either the whole Amidah (standing prayer) or part of it if he is still in the middle of praying, does he go back or not? The consideration here is that perhaps by going back, he will delay the start of the chazarah (repetition) and cause the kahal (congregation) to have to wait.
If he makes the mistake and realizes it right afterward—for example, he forgot to say Ya'aleh VeYavo (May it arise and come) and remembers right away in Modim (We give thanks)—and he can easily go back and correct it by adding only a few seconds, maybe half a minute, then of course he should go back because it is not going to cause a delay.
But if, let's say, the person is in Sim Shalom (Grant peace) and he forgot to say Barech Aleinu (Bless us), which would make him have to go all the way back to the early part of the middle section of the Amidah, adding maybe several minutes, then he has one of two options. Either he can motion to somebody else to take over the chazarah, and he goes back to the tefilah (prayer) so as not to delay the kahal, or Shulchan Aruch rules that he can complete the Amidah without going back and rely on the repetition of his Amidah to satisfy the requirement that he had missed.
Certainly, if he completes the Amidah, he would not be required to go back to the beginning and repeat the whole Amidah over; he could for sure rely on his chazarah to count for his personal tefilah.
If, however, he missed an element in the first three—for example, he didn't say HaMelech HaKadosh (The King, the Holy One) during the ten days of Teshuva (repentance), but said HaEl HaKadosh (The God, the Holy One) instead—then, since that's a quick fix, he goes right back to the beginning of the Amidah. He would be required to go back and repeat, and it won't cause such a big delay. If he is concerned it will cause a delay, then somebody else should take over for the chazarah.