Andrew Fulford has some thoughtful reflections on how far Jesus' impeccability extended during his earthly ministry. Clearly an orthodox view of the Incarnation requires Jesus not sinning, but could he have had false beliefs as he was growing and learning? Andrew argues no. Andrew thinks any sense in which Jesus might have made an error would make the Incarnation contradictory. (He says parodoxical, but the Incarnation is paradoxical no matter you say about this issue; I assume he means outright contradictory.)
I'm a little worried about what Jesus' growth and learning involved if he never made any errors whatsoever. In particular, what could his language acquisition have been like? The normal, I would say correct, path to language development involves learning certain rules that one eventually has to unlearn in order to master the next stage of language-learning. Children regularly make certain errors. At least they count as errors when you compare it to fluent use of the language by an adult. These errors actually might count as correct use of the stage of language understanding that the child has. If we think of it that way, then maybe Andrew's thesis turns out ok. If such errors aren't really errors, then Jesus could have learned the languages he spoke (which probably included Aramaic, Greek, and Latin) with all the standard errors children make, without them counting as the kind of error Andrew is worried about.