I have written in various places, as has my husband, Tim, about the argument for the historicity of the gospels and Acts from undesigned coincidences. I won't try to link all of those posts, but you can start here, here, and here. (One of these has links to a series Tim did on the subject.)
A related but slightly different line of evidence is the argument from unexplained allusions.
As it happens, one half of many an undesigned coincidence is an (otherwise) unexplained allusion. For example, Luke tells us that Pilate, prompted by the Jewish leaders' charge of sedition against Jesus, asks Jesus if he is a king. Jesus confirms that he is, and Pilate, surprisingly, returns and tells the crowd, "I find no fault in him." This is an unexplained turn of events which apparently alludes to some part of their conversation not recorded in Luke. And indeed, we find in John that Jesus says more, telling Pilate, "My kingdom is not of this world" and assuring Pilate that his disciples are not going to fight to deliver him. The extra information in John explains what is unexplained in Luke: Why did Pilate say that he found no fault in Jesus after Jesus had apparently confirmed the charge that he was setting himself up as a king? The two passages fit together like two pieces of a puzzle to give us a realistic picture of a portion of Jesus' trial. Each one is written in exactly the casual way one would expect to find from a witness (in Luke's case, whatever witness was his source) who does not stop to explain every bit of his story but merely tells events as they now come back to him.
Sometimes, we find an unexplained allusion for which we never get an explanation. This, too, is evidence for the historicity of the text. In Mark (and only in Mark), we find the following, in a list of Jesus' twelve disciples:
And Simon he surnamed Peter; And James the son of Zebedee, and John the brother of James; and he surnamed them Boanerges, which is, The sons of thunder. (Mark 3:16-17)
Nowhere else are we told that Jesus called James and John the sons of thunder. Nowhere is this surname expressly explained. In particular, it is not explained in Mark, and even more particularly, it is not explained when Mark mentions the nickname. Mark does not introduce this nickname (nor Simon's) by way of a story, nor does he follow either of them with a story in this passage. Not so much as an explanatory phrase in passing tells us how the nickname "Boanerges" came to be given by Jesus.
We may guess that a clue to "Boanerges" is found in Luke 9:53-54, where James and John suggest calling down fire on a Samaritan town after the people there refuse to receive Jesus. Perhaps this is an indication of their personalities. But that, though interesting, is not clearly the correct explanation. If Jesus gave the nickname earlier in his ministry, it cannot be the only explanation. There could in any event be many possible reasons for Jesus to give the nickname. One must consider that John in particular was almost certainly quite young at the time, possibly only a teenager. Anyone who has ever known teenage boys or even college-age young men can think of plenty of reasons for calling a pair of brothers "the sons of thunder"! Maybe they were especially loud and boisterous. Maybe they scuffled with each other and with the other disciples. Maybe the Samaritan incident was only one in a series of cases where they thought it would be cool to blow up a city--boom! The sons of thunder.
The fact is that we simply don't know for sure. But that is itself a fascinating point. The passage in Mark is a list of the names of Jesus' disciples. That's it. It's just a list. In its very bareness lies its verisimilitude. What other reason than truth, and truth remembered by one in a position to know, could there be for telling us en passant that Jesus nicknamed James and John Boanerges, the sons of thunder? The detail serves no literary purpose. It serves no theological agenda. Of course there must have been a reason, maybe several reasons, for the bestowal of this nickname, but Mark, following his source (probably Peter), feels no compulsion to tell us what that reason is. Perhaps Mark never found out from Peter what the reason was. The detail is taken to be worth mentioning in itself, but only as part of the list of the disciples. This is who they were. This was what Jesus, the Master, called them.
This is just one small, internal mark of truth (no pun intended) in the gospels. There are so many others. I want to suggest, too, that laymen may be cuing to these marks of truth unconsciously. The gospels read like memoirs. They don't read like abstract, ahistorical, pious "holy books." They don't read like made-up stories. It is no exaggeration to say that the relationship between the disciples who wrote or served as sources for the gospels and Jesus was like the relationship between Boswell and Johnson. Jesus emerges as an historical figure not only real, but real in remembered detail. I believe that people can see this even if they can't articulate what they are seeing.
This is in itself evidence for the truth of Christianity. For if this, this story, including the miraculous parts, including Jesus' resurrection and their meetings with him afterwards, is really what the disciples were claiming, and if they really were close to the events, really in a position to know, and if they were willing to die for their testimony, why? What explanation is there for it, since they had so little to gain and so much to lose?
It is little details such as this one in Mark that, in the aggregate, blow to smithereens the fantastical ideas of literary biblical criticism that would give us four gospels built by layers of unhistorical accretion.
The evidence for the historicity of the gospels (and of other parts of Scripture as well) is so strong in part because it is varied in type. Apologists should add the unexplained allusion to their toolbox of internal evidences.