Mark 2:25-26
25 And he said unto them, Have ye never read what David did, when he had need, and was an hungred, he, and they that were with him?
26 How he went into the house of God in the days of Abiathar the high priest, and did eat the shewbread, which is not lawful to eat but for the priests, and gave also to them which were with him?
Above, in the Gospel of Mark, Jesus references a story from 1 Samuel chapter 21 where David sinned by eating consecrated bread that was only for the priests:
1 Samuel 21:1-6
1 Then came David to Nob to Ahimelech the priest: and Ahimelech was afraid at the meeting of David, and said unto him, Why art thou alone, and no man with thee?
2 And David said unto Ahimelech the priest, The king hath commanded me a business, and hath said unto me, Let no man know any thing of the business whereabout I send thee, and what I have commanded thee: and I have appointed my servants to such and such a place.
3 Now therefore what is under thine hand? give me five loaves of bread in mine hand, or what there is present.
4 And the priest answered David, and said, There is no common bread under mine hand, but there is hallowed bread; if the young men have kept themselves at least from women.
5 And David answered the priest, and said unto him, Of a truth women have been kept from us about these three days, since I came out, and the vessels of the young men are holy, and the bread is in a manner common, yea, though it were sanctified this day in the vessel.
6 So the priest gave him hallowed bread: for there was no bread there but the shewbread, that was taken from before the Lord, to put hot bread in the day when it was taken away.
The alleged problem is that Jesus says that it was in the days of Abiathar the high priest, whereas Ahimelech, Abiathar's father (1 Samuel 22:20) was the priest when the event took place.
Firstly, "in the days of Abiathar" is a general statement, and absolutely applies to the time period that the event took place, seeing that Ahimelech was killed in the next chapter (1 Samuel 22:16-18) and only Abiathar survives the massacre.
Secondly, it's possible that there were multiple high priests.
There is at least one explicit example of this happening in Scripture:
Luke 3:2
2 Annas and Caiaphas being the high priests, the word of God came unto John the son of Zacharias in the wilderness.
I find it much more likely though that Christ was making a general statement in regard to the time the event took place, so saying "the days of Abiathar" is completely valid.
This would be like saying "telephones were invented in the days of Abraham Lincoln". Even though they were invented about 10 years after he died, he is a well-known figure that lived about that time that can serve as a frame of reference.