Problem: Jesus names Abiathar as high priest when he wasn't

At one point fairly early on in his ministry, the synoptics record that Jesus was questioned about an apparent breach of the sabbath. This is Mark 2:25-26:

And he said to them, 'Have you never read what David did when he and his companions were hungry and in need of food? He entered the house of God, when Abiathar was high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and he gave some to his companions.' (NRSV)

(I've used the NRSV here since it gives the problem in its most direct form, but we'll look at another way to translate it later.) Jesus is here referring to an incident described in 1 Samuel 21:1:

Then David came to Nob to Ahimelech the priest. And Ahimelech came to meet David trembling and said to him, "Why are you alone, and no one with you?" (ESV)

It certainly seems that either Jesus or Mark has made a mistake and named the wrong priest. However, since the Old Testament verse doesn't actaully say that Ahimelech is high priest, it's possible to argue that in fact Abiathar was high priest at that time, and Jesus is merely setting the date by mentioning him, even though he's not involved in the story.

However. The standard view of Bible scholarship is that Ahimelech was indeed high priest at the time (this is the view of the NIV Study Bible, and the NET Bible, for example). Abiathar, son of Ahimelech, is only introduced to the reader some time after the bread incident, at 1 Samuel 22:20. Bible scholars seem to agree that, although Abiathar was one of around 85 priests at this point, he was not yet a high priest. Abiathar is never described as "high priest" in the Old Testament, but Bible scholars seem to infer that he became a high priest at 1 Chronicles 15:11-12 when he and one other priest are specially summoned to serve David and carry the Ark of the Covenant.

Translation issues

And he said to them, "Have you never read what David did, when he was in need and was hungry, he and those who were with him: how he entered the house of God, in the time of Abiathar the high priest, and ate the bread of the Presence, which it is not lawful for any but the priests to eat, and also gave it to those who were with him?" (ESV)

The motive for this is to suggest that, since Abiathar had been born by the time of the bread incident, it can therefore be described as "the time of Abiathar the high priest". I would question this: it seems to me like using "the time of President Reagan" to refer to the 1960s, which you would never do. But perhaps it works better in ancient Greek.

Why I think this is an error

Regardless of how the verse is translated, the fact remains that the high priest in the Old Testament story is Ahimelech. And so, if Jesus was going to mention a high priest, I'm sure it would be Ahimelech. There's very little reason for him to mention Abiathar.

Matthew and Luke, who both used Mark as a source, apparently both detected and eliminated the error, as shown by this comparison of the three synoptic gospels. They are all basically the same, but Matthew and Luke wisely delete the clause "in the time of Abiathar the high priest".