and

The Jews said the Christ is to come from Bethlehem in John 7:42, not knowing that Jesus was born in Bethlehem.

When they heard these words, some of the people said, “This really is the Prophet.” 41 Others said, “This is the Christ.” But some said, “Is the Christ to come from Galilee? 42 Has not the Scripture said that the Christ comes from the offspring of David, and comes from Bethlehem, the village where David was?” 43 So there was a division among the people over him. 44 Some of them wanted to arrest him, but no one laid hands on him.
(John 7:40–44, ESV)

Here they are arguing over who Jesus is, but when Christ comes from Bethlehem is brought up, no one mentions he was born in Bethlehem.

John wrote his Gospel after the synoptics and seems to avoid repeating what is in the Synoptic Gospels as if expecting his readers to already be familiar to them. (When John refers to what is ‘not written’, in his gospel account, does he mean, in part at least, the parables of Jesus?)
Thus, John would expect his readers to know that Jesus was born in Bethlehem.

Did John point out the mistakes the Jews made related with Jesus and his teachings expecting the reader to catch the mistake?

Another example; are there more?

John 8:33 Why does Jesus not correct the Jews when they said they they were never slaves of anyone?

This style would take up less room on the scroll and engage the reader.