This is his “evidence:”

The filmmaker rests his case on four main points. First, he says, recent Biblical scholarship argues that Mary Magdalene’s real name was Mariamene, a common first-century derivative of Miriam. Second, DNA tests show that microscopic human remains scraped from the Jesus box and the Mariamene box are not related, at least not matrilineally, leaving open the possibility that the two humans whose bones were once in those boxes were married. Third, the patina on the Talpiot ossuaries-that is, the mineral crust accumulated over centuries-matches that of the James box. This “discovery,” if provable, is complicated but critical to Jacobovici’s argument: the match means, he says, that the James ossuary originally lay in the Talpiot cave, thus answering questions about the James box’s provenance. It also increases the probability that the tomb belongs to the Holy Family. Jesus had four brothers, according to the Gospel of Mark; two of their names-Joseph (or Jose) and James-were found in the Talpiot tomb.
The technique Jacobovici uses to “prove” the match between the James ossuary and the Talpiot tomb is a technology he calls “patina fingerprinting,” which he and his coauthor Charles Pellegrino (a scientist who helped Cameron write “Ghosts of the Titanic”) essentially invented for the purposes of this project. By comparing the mineral content of shards from the Talpiot ossuaries with shards from James, and by looking at them under an electron microscope with the help of a CSI specialist, Jacobovici and Pellegrino say they have a match. But do they? It’s impossible to know for sure. For John Dominic Crossan, leader of the liberal Jesus Seminar and author of “Excavating Jesus,” the biggest questions relate to the early break-in: who vandalized the cave, when, what did they do there and why?
The fourth part of Jacobovici’s argument is statistical. Individually, he concedes, all the names on the Talpiot ossuaries are common. Charlesworth of Princeton Theological Seminary says he has a first-century letter written by someone named Jesus, addressed to someone else named Jesus and witnessed by a third party named Jesus. But the occurrence of these names in one place, with these specific idiosyncrasies, how likely is that? Andrey Feuerverger, a statistician at the University of Toronto, came up with an estimate: 600-1 in favor of the tomb’s belonging to the Holy Family.

As I demonstrated here, these names were very popular, in fact “25 percent of women in Jerusalem, for example, were called Miriam or a derivative.”And according to Crossan, “after Simeon, the most popular name on ossuaries (19 of 147 names, male and female, on known ossuaries) with Jesus almost as common (10 of 147). And the most frequent name after Salome is the variously spelled Mary (20).” Evidence based on names really should be excluded but then what are you left with? Maybe a connection to a discredited tomb? And the evidence that a man named “Jesus” and a woman named “Mariamene” were not related and from this he gets that this is Jesus of Nazareth? Weak, very weak. I bet if he were in a court of law, it would have been thrown out. Especially, when it’s weighed against the number of eyewitnesses in the Bible to the empty tomb.
Plus, there’s this:

Pfann is even unsure that the name “Jesus” on the caskets was read correctly. He thinks it’s more likely the name “Hanun.” Ancient Semitic script is notoriously difficult to decipher. [Amen to that!]
[…]
Archaeologists also balk at the filmmaker’s claim that the James Ossuary _ the center of a famous antiquities fraud in Israel _ might have originated from the same cave. In 2005, Israel charged five suspects with forgery in connection with the infamous bone box.
“I don’t think the James Ossuary came from the same cave,” said Dan Bahat, an archaeologist at Bar-Ilan University. “If it were found there, the man who made the forgery would have taken something better. He would have taken Jesus.”

I’ll probably watch the show and yell at the screen the whole time (“Do these people think we are that stupid?”). It airs on March 4 on the Discovery Channel.
You can view their Today show appearance here.
BTW, I found this statement rather odd:

“They are huge, but they are not necessarily the implications that people think they are,” Jacobovici said. “For example, some people are going to say, ‘This challenges the Resurrection.’ I don’t know why. If Jesus rose from one tomb, he could have risen from the other tomb.”

He really doesn’t have much knowledge of Christianity because we believe that Jesus’ reurrection was a bodily resurrection and that his tomb should be empty. We also contend that he ascended into heaven and is seated at the right hand of God the Father. If he died and did not raise again, our hope is in vain because we are still in our sins. God did not accept the offer of Jesus in our place.
Christianity is entirely based on the resurrection of Jesus, if that is ever disproved, true Christianity, Christianity based on what the word of God says, would cease to exist. This claim by Cameron is not even close to disproving Christianity.
Update: I’ve been blogging a lot about this:
Oh no! How will Christianity survive?
Update on the tomb of some guy named “Jesus”
The Tomb of “Jesus?”
Cameron’s “evidence” that it’s Jesus’ tomb
Jesus, son of Joseph
“Jesus” tomb links
Documentary does not challenge Christian beliefs