Geography. If the Gospels were written by someone who didn’t live in the local area, they would never be able to describe Palestinian geography with such accuracy. No sources that we know of—not Josephus, Philo, Strabo, anyone—could have given the writers the details they mention, often in passing: villages, bodies of water, hills, landscapes, and so on. When you compare the four Gospels with the Gnostic Gospels (Judas, Thomas, Philip and co), the disparity in geographical awareness is extraordinary.

Topography. The same is true for the very incidental (to the extent that you barely notice them) mentions of topography: up to Jerusalem, down to Jericho, down from Cana to Capernaum, and so forth. Much of this information is available in no other sources, as far as we know, and this suggests the writers were very well acquainted with the landscape.

Names. Richard Bauckham has done a lot of work here, and Peter summarises it well: the distribution of personal names we find in the Gospels corresponds extremely well to what we know of Palestinian Judaism on the basis of other sources (including Josephus, the Dead Sea Scrolls, rabbinic texts and ossuaries). Jews in other parts of the empire had very different naming habits, so nobody from outside the area would have invented plausible names with such accuracy.

Disambiguation. The previous point is strengthened by the practice of disambiguation in the Gospels. Some characters are repeatedly disambiguated (Mary the mother of Jesus, Mary Magdalene, Mary mother of James and Joseph; Simon Peter, Simon the Zealot, Simon of Cyrene; Jesus of Nazareth, Jesus son of David, Jesus the Galilean; John the Baptist, John the son of Zebedee; and so on). Many others never are. The names which are disambiguated are those which would need to be clarified in Palestine, but not elsewhere, and this adds to the veracity of the accounts.

Judaism. The awareness of Jewish language, law, Scripture and culture is clear throughout the Gospels. It indicates not only a high degree of familiarity with Judaism, but also (perhaps) an early date of composition, since the “parting of the ways” that followed the destruction of the temple would make such a correspondence far less likely.

Botany. How did the authors know that the rabbis tithed dill and cumin? How did they know that sycamores grow in Jericho?

Finance. I love this one: we encounter a whole group of tax collectors in Capernaum (Matt 9:9-10; Mark 2:14-15). What none of the Gospels mention is that Capernaum was in a key location on the border of the territory of Herod Antipas, and therefore exactly the sort of place we would find tax collectors. Jericho, likewise, is home to a very wealthy chief tax collector (Zacchaeus), which is just what we would expect of a border town. The Gospel writers know the local tax systems.

Language. Matthew, Mark and John all show clear signs of being familiar with the local language, in ways that could not simply be drawn from other sources. The word hosanna is a fascinating example, because the evangelists not only get its counterintuitive usage right (the word originally meant “save”, but in the Gospels and in later Jewish sources it is more of a cry of praise), but also its pronunciation, which differs from the original Hebrew hoshianna. Neither of these facts would be available to someone from researching or reading books.

Customs. Celebrating the Passover inside Jerusalem, even when you weren’t staying there; singing a hymn before going to the Mount of Olives; priestly servants carrying a club; tearing clothes in response to the charge of blasphemy. Once again, the writers show first-hand knowledge of Jewish customs that could not have been gained through second-hand research.

Undesigned coincidences. On several occasions, different Gospel writers provide details that make sense of something another Gospel says, yet in a way that is so subtle most people miss it (and certainly not in a deliberate fashion). John and Luke tell completely different Martha and Mary stories, but they both present Martha as a practical person and Mary as much more contemplative; each sheds light on the other, but without being designed that way. Mark calls James and John “sons of thunder”, and Luke tells us they want to call down fire from heaven; both illuminate the other, but almost accidentally. When we read John, we wonder why Jesus asks Philip in particular to buy food for the massive crowd, a fact which we can only make sense of when we look at Luke, and find that the miracle took place near Bethsaida (Luke 9:10), Philip’s home town. And so on.

Embarrassing inclusions and omissions. Jesus calls his followers “evil” (Matt 7:11), calls Gentiles “dogs” (15:26), instructs his disciples to listen to the Pharisees (23:3), and dies asking why God has forsaken him (27:46). No one fabricating these stories would invent these sorts of things. Flipping the comment round, it is also unimaginable that an invented Gospel, written to bolster the early church in the 70s or 80s, would omit any mention of circumcision, Gentiles in the church, or ordering Christian worship. The Gospels do not look like they would if someone was inventing the story after the fact.

Deliberate formal contradictions. Finally, in response to the argument that the Gospels preserve contradictions between them, Peter makes the telling point that each Gospel contains within itself examples of contradictions which are clearly deliberate, in order to make the reader think. He gives a number of examples from John: Did people believe in Jesus when they saw his signs, or not? Did they know where he came from, or not? Is Jesus’s testimony true if he bears witness to himself, or not? Does Jesus judge no one, or does he judge all the time? Did he come into the world to judge it, or not? If Gospel writers deliberately preserve these kinds of tensions, or paradoxes, why should we think that tensions between the Gospels are a sign of unreliability?

I could go on. There is an excellent discussion of whether we have the actual words of Jesus, in which Peter makes some important comments about the lack of the punctuation marks by which we indicate paraphrases, like “...” and “[…]” There is a helpful treatment of miracles, and the resurrection in particular. And the whole book is written in accessible English, in an engaging and humorous style, in 140 pages. Check it out.