Although the names of Jesus and Joshua are different in English translations, they are both the same name in Greek and Hebrew. In fact, Jesus seems to have been named after Joshua. While the Gospels of Matthew and Luke have completely different nativity stories from one another, one thing they both agree on is that Jesus was named by an angel. In Luke, the angel Gabriel appears to Mary and says "You shall bear a son, and you shall call his name Jesus" (Luke 1:31). In Matthew, the angel appears to Joseph, so the wording only differs by a pronoun: "She shall bear a son, and you shall call his name Jesus." (Matthew 1:21) Luke goes on to call Jesus "son of the Highest" (Luke 1:32), perhaps with Joshua son of the Lord in mind.
In the apocryphal Protevangelium of James, the parents of Mary were sterile. So Mary's father Joakim goes to the desert to fast for forty days, while Mary's mother Anne prays to get pregnant in a fertility rite setting - sitting under a tree, wearing a headband, and looking at a nest of sparrows. Angels appear to both of them promising a miraculous birth. Mary's mother Anne (based on Anne, the mother of the prophet Samuel in the Old Testament, also compare 1 Samuel 2:1 with Luke 1:46) vowed to give her child to serve the Lord. Accordingly, when Mary was three years old, she was given to the temple where she was fed by an angel. Perhaps her being given to the temple is an echo of the "hallowed ones" or temple prostitutes of the Hebrew Bible. When she turned twelve, the priests were worried she would pollute the temple (by menstruating) so they gave her to the elderly widow Joseph. While spinning thread to make a curtain for the temple, Mary is visited by an angel and becomes pregnant with Jesus.
In a footnote, Levin points out that the Gospels (Mark 11:8-11, Matthew 21:8-10, John 12:12-13) confuse the autumn festival of Tabernacles where palms were waved and people cry "please save" with the spring festival of Passover. He explains their ignorance of Jewish customs by supposing the authors of the Gospels wrote after the Temple was destroyed (70 CE) and they did not attend synagogues either. I think a better explanation for why the Gospels are ignorant of Jewish customs is that they were not written by Jews, but hey, that's just me.
While Jesus recreates most of the miracles performed by Elisha and Elijah in the book of Kings, one miracle is conspicuously absent: making a sterile woman fertile (although Luke has John the Baptist born to aged parents similar to Abraham and Sarah, this happens before the birth of Jesus). Levin supposes that Jesus's miracle of turning water into wine at a wedding (John 2:1-11) could be thought of as a fertility miracle since having plenty of wine at a wedding makes the occasion more joyous which in turn makes it more likely that the marriage will produce children, but I think this is stretching it a bit.
In another footnote, Levin points out that the name of Jesus's mother is never given in the Gospel of John, and in fact her name being Mary as it is in the other Gospels is unlikely since her sister is named Mary. While it wouldn't be unusual in Roman families to have two sisters both named Mary, this wasn't done amongst Jews. Does this indicate that John had a different name in mind for the mother of Jesus, perhaps edited out later to conform with the other Gospels, or is it an indication that the Gospel writer was Roman?
Jesus is called the "son of David" when he heals the blind or performs exorcisms (Matthew 9:27, 15:22, 20:30-31, Mark 10:47-48, Luke 18:38-39), which implies that David was known for performing such miracles himself. David does cure Saul of an evil spirit (1 Samuel 16:14) and the Talmud tells us he was a gynecologist (Tractate Berakoth 4a). However, David did not heal the crippled Mephibosheth, although he did provide for him (2 Samuel 9:1-9). Perhaps with this in mind, Jesus is not called the "son of David" when he heals the lame (Luke 5:17-26, John 5:1-15). The only other time Jesus is called the "son of David" is during his triumphal entry into Jerusalem during Passover (Matthew 21:9-16).
Although Jesus is called "the Anointed One" (i.e. Christ), there is no depiction of him actually being anointed. The closest the Gospels come is when a woman pours perfume on him (Matthew 26:7, Mark 14:3, John 12:3, Luke 7:36-50) although Jesus himself says this is for his burial (Matthew 26:12, Mark 14:8), not for anointing. Acts 10:38 is the most explicit reference to an act of anointing, although this refers to being anointed by spirit. Levin muses that the anointing had to be kept secret since when the disciples of Jesus say he is the anointed one, he instructs them to tell no one (Matthew 16:16-20, Mark 8:29-30, Luke 9:20-21). Calling himself the anointed one was tantamount to calling himself King of the Jews, which is what ended up getting him into trouble. Jesus not being officially anointed like King David makes him more like Joshua who wasn't anointed either. This is because Joshua was from an earlier time when leadership was bestowed by the laying on of hands rather than anointing (Numbers 27:18-23).
Just as Joshua's spies in Jericho stay at the house of Rahab the prostitute (Joshua 2:1), Jesus kept the company of prostitutes. Joshua's miracle of destroying the walls of Jericho (Joshua 6:1-20) finds a possible correspondence in Jesus's claim that he will destroy the temple and in three days build another ( Mark 14:57-59, Matthew 26:60-61, John 2:19). Although Levin doesn't mention it, Joshua's miracle of making the sun stand still (Joshua 10:12-13) may correspond to the darkening of the sun at the death of Jesus (Matthew 27:45, Mark 15:33, Luke 23:44-45). Levin claims Jesus was meant to be a military leader like Joshua and plays up the militant aspect of Jesus, pointing out that the followers of Jesus were armed (Luke 22:49), one of Jesus's followers cut off a servant's ear (Mark 14:47, Matthew 26:51, Luke 22:50, John 18:10), Jesus tells his disciples to sell all they have to buy swords (Luke 22:35-36), and Jesus says he came not to bring peace, but a sword (Matthew 10:34-36). I must admit that all these similarities seem more like parallelomania than actual evidence of a correspondence to me.
In direct contradiction to his own introduction, Levin uncritically accepts the Gospel accounts as history rather than literature and cherry picks out passages that match his view of Jesus as a guerilla leader. He ends his book by telling us that Jesus being called the son of God was originally due to his being a great man, not due to being thought of as God's literal offspring.