There's an incident in which a centurion's servant is healed through faith alone. But there's a discrepancy between Matthew and Luke. This is Matthew 8:5-6:
By contrast, this is Luke 7:2-3:
Matthew and Luke's versions seem to contradict each other. Various infallibilists respond that "a centurion came forward to him" means simply that he sent messengers. This explanation would be more convincing if Matthew had used different wording, but "came forward to him" is a very odd way of saying "sent messengers".
Infallibilists like to compare Matthew's words to another passage where "X did Y" means "X got others to do Y". This is John 19:1:
Yes, in this case it's clear enough that someone else did the actual work. That's obvious. On the other hand, it's so far from obvious in Matthew that, if Luke's gospel didn't exist, nobody would have thought the centurion sent messengers.