Sure the KJV has a couple of errors, but no doctrinal errors
Actually, there is at least one doctrinal error in the KJV.
Even when translators get the words right, they still have to punctuate the sentence. The Greek manuscripts not only had no verse numbering, but they also weren't punctuated. There are more than a few commentaries by Chrysostom and other Greek commentators discussing where they should assume the pauses to be.
Punctuating a passage incorrectly can lead to heretical readings. For example, from their commentaries we know that most Greek Church Fathers, and certainly Chrysostom, understood John 5:27-28 to read:
[The Father] hath given Him [the Son] authority to execute judgment also. That He is the Son of man, marvel not at this ...
In the 3rd century, however, the heretical Antiochian bishop Paul of Samasota used a different reading of the same passage to support his theology contesting Christ's divinity. Unfortunately, his reading is the one that the KJV translators chose to render:
[The Father] hath given him authority to execute judgment also, because he is the Son of man. Marvel not at this ...
In the Orthodox interpretation, the passage says that we should not be surprised that the Son has authority to execute judgment because he is also the Son of man. In the heretical interpretation, repeated in the KJV, the passage says that the Father had to give Him the authority because he is the Son of man. John Chrysostom, writing (in Greek) from Constantinople in the late 4th century, explains:
He did not receive judgment 'because' He was Man - since then what hindered all men from being judges? - but because He is Son of the ineffable essence, therefore is He judge. So we must read, 'That He is Son of Man, cease marvelling at this.' Paul of Samasota renders it not so, but how? 'He did give to Him authority to be executing judgment, because He is Son of Man.' (
Homily 39,
Homilies on the Gospel According to St. John)
(Paul of Samasota's teaching - known as Paulianism - was condemned by at the 1st Ecumenical Council in 325 and by several local councils before that).
Probably it is an unintentional error and I am not aware of any more like this in KJV, but I thought I would point out that is not strictly true to say that the KJV does not contain any doctrinal errors. It seems, though, that almost all the New Testaments out there contain the same error (e.g. NIV, NASB, Douay-Rheims). The only translation that I am aware of that does not contain the error are is the hyper-literal
Orthodox New Testament, translated and edited by a group of schismatic Greek Orthodox nuns in Colorado