"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?"One issue here is whether this was Ahimelech at all, as when Jesus recounts this story in Mark 2, he calls the priest "Abiathar". While this issue doesn't come up until the next chapter, it seems clear to me that it must be related: Abiathar was another priest, and depending on which verse you read, he was either Ahimelech's son or father. What's going on? I'm not sure.
One thing that I think can safely be said is that it's certainly not uncommon for a father and son to both serve as priests at the same time. (There is often more than one priest, but only one high priest*, which in this case was Abiathar.) That being the case, David probably came to both, but talked specifically to Ahimelech. Jesus says it was "the days of Abiathar the high priest", but doesn't say that David talked to Abiathar. But who is the father? I think that's a question that can be answered, but I'm having a hard time figuring it out. I decided not to obsess over it, since whatever the answer is, the contradiction is still there, probably representing a scribal error. I'll come up with a verdict on the matter, but I think I'll let it drop for now, since it's a tough nut to crack.
The easy issue to address is that of whether or not David was alone. Yes, the priest comments that David is alone, while Jesus says he was travelling with others. I think this is almost silly though, and once again requires only looking at immediate context. Down in verse four, shortly after David asks for bread, the priest refers to "the young men" whom he assumes will be eating the bread. David is not travelling alone, but at the moment that he comes to the priest, he doesn't bring anyone with him into the house. In the immediate context of Jesus' comments on the matter, note that Jesus says "he entered the house", not "they entered the house". So was he alone? Yes, at the moment, but not on the overall journey.
So David gets the bread, but only after he assures the priest that neither he nor any of the men with him have recently had sex. The SAB seems to be saying that this is a bit sexist, and I'm inclined to agree, but I'm not sure what the reason for the priest saying this is. This is an unusual circumstance, David taking holy bread, and I certainly don't know what rules ought to be followed. It may be that the priest made the rules up.
The remaining issues in this chapter are mostly ones I have addressed previously. The killing of Goliath was in chapter 17, and the strange chant about body counts in chapter 18. The only thing not yet addressed is the story of David pretending to be insane, which I'm not sure what there is to say about it. Absurd? Well, he's pretending to be crazy, so crazy and absurd seem to me to be things that tend to go hand-in-hand. David's intention was to protect himself and make himself seem a non-threat to the Philistines, and apparently he succeeded, so what can I say?
* I know of a single exception to this general rule; I'm sure we'll get to it when we come across the particular verse in the New Testament.