According to atheist/agnostic New Testament Scholar Bart Ehrman, Mark 2:26 proves the Bible is not divinely inspired because Jesus, the infallible God incarnate, supposedly demonstrates Biblical illiteracy. This is because Jesus says "in the days of Abiathar the high priest". However, at the time of the event in question, Abiathar was not serving as high priest; his father, Ahimelech was.
Although this argument sounds logical, it's really just clutching at straws. Note first that Jesus did not say Abiathar was acting as high priest at the time. He simply said "in the days of Abiathar the high priest". This statement is accurate. At the time of the event, Abiathar did exist, and was, in fact, involved in this very incident (1 Samuel 22:20-23). Abiathar inherited his father's position of high priest later on.
In English, we use similar terminology. How many of us will refer to ancient rulers as "Prince Arthur" or "Princess Elizabeth"? Even if we speak of them before their rule, most of us still refer to them as "King Henry" or "Queen Mary" etc. As long as they held the title at some point during their life, it is entirely legitimate to refer to them by it. Obviously, there are exceptions for their present ranks. Prince Charles, for example, is not the king of England yet, and may never be, thus it is appropriate to refer to him as Prince Charles. If, however, he ascends the throne, it will be appropriate for future historians to refer to him as King Charles, even if they were to talk about his early life.
Thus, Jesus was not making a Biblical error. Rather, He was referring to Abiathar by the title he was best known for. He was best known as a high priest, and thus it was legitimate to refer to any point during his life as "in the days of Abiathar the high priest". Now, had Jesus said "when Abiathar was serving as high priest", that would have been problematic. However, as He only said "in the days of Abiathar the high priest", and was, in fact, referring to a time very shortly before his appointment as high priest, that's totally fine. It makes perfect sense to refer to him as high priest, and no sense to literally change your entire religion over such a minuscule detail.