You are not allowed to let an apikorus be the chazzan. (e.g. denies Torah min hashomayim, reward and punishment, techias hamaysim or the future redemption.) If it is beyond your control, at least do not respond after his tefillos. (MB 2)
A chazzan who gets confused in the middle of the repetition and cannot continue – or he feels too weak to continue, another person should take over from the beginning of the beracha that the first person could not finish. This applies only to the middle berachos. But if it happened in the first 3 berachos, then the substitute begins again from the start of Shemoneh Esray. If it happened in the last 3 berachos, then the substitute goes back to R’tzay. (ShA 2 – MB 10)
On Yom Tov, when many piyuttim may have been said already, be sure to take over at the beginning of the main beracha that starts that section of Shemoneh Esray. The substitute chazzan does not repeat the piyuttim. (MB 10)
Lechatchila, choose a substitute who was listening to the first chazzan’s repetition until now. He should not refuse the request to take over. (MB 8,9)
Any mistake for which an individual would have to daaven again, a chazzan would also have to daaven again if he makes such a mistake during the repetition. An exception: forgetting to mention Shabbos at Shacharis when Yom Tov falls out on Shabbos. (ShA 3 – BeH “v’hochi”)
If the chazzan made a mistake during his silent Shemoneh Esray, he may rely upon his repetition to fix it. Even if the mistake was in the first 3 berachos, he can rely upon the opinion of the Tur to continue on. (ShA 4 – MB 17)