Is it possible that this episode takes place during the events of 316? Christian is telling Vincent to wake Jack the second time he returns to the Island? I realize that Christian wasn't shown in 1970's, but is it possible he was there?
It appears that Vincent, as he passes through the jungle, moves past a smoky substance in the distance. It could be smoke from the wreckage, could be the Smoke waiting to see what Vincent and Christian do, or it could be the Smoke prior to its transformation into Christian.
Possible, but Christian acts way too human in this mobisode. He uses "my son," which isn't proof that it isn't the Monster or Jacob controlling him, but they'd most likely say "Jack." And he speaks to himself after the dog leaves, for our benefit of course, but the Monster or Jacob wouldn't say it or make him say it. People talk to themselves all the time though. It helps focus the mind.
However, Christian's presence in "White Rabbit" is clearly inhuman, so it could mean this presence of him is also not himself.
Jacob has taken over Christian's body, and thus has Christian's memories, so he refers to Jack as his son.
If this is either a form of the Monster or Jacob, then it appears that Locke was correct and the Island did choose Jack by saying, "He has work to do."
Christian Shephard is some sort of supernatural presence that opposes Jacob, and appeared on the island once 815 crashed. This is apparent by his knowledge of Jack's survival and location after the crash. Not to mention he is able to communicate effectively with Vincent, who willingly follows his orders having never seen him before.
Christian is the only person who was dead when 815 crashed. If he is the spirit of "new" Jacob, it is possible Locke will be the spirit of "new" Jacob when he turn back to the Island as dead in the 6th season.
Jack "has work to do" to get the survivors of 815 rescued, which directly opposes when Walt (who may possibly be a manifestation of Jacob, the island, or the smoke monster) informs Locke he "has work to do" to keep rescue away from the island.
Jack's work to do is to help the passengers still in casualty from the wreckage.
Jacob, acting through Christian, wants Jack to save the survivors of 815 because Jacob wants them to replace the current group of Others on the island. That is why, for instance, Christian got Jack to follow him to the caves in Season 1 - so that the survivors would have a safe place to live. At the same time that Jack is leading the survival effort in the short-term, a task for which he is better suited than Locke, Locke is being groomed by Jacob to eventually assume long-term leadership of the survivors, much like Ben currently leads the Others, based on his superior communion with the Island.
Christian IS Jacob.
Jack's work may be to save one particular survivor. I can't remember everyone he directly or indirectly saved in the Pilot but Claire and Hurley stick out in my mind. Perhaps the Island wanted either or both to be rescued and only Jack could do that.
It seems like the work was important as Christian wanted Jack to be woken up then instead of later so that suggests the work was immediate rather than later
Jack also saved Rose in the Pilot, who seems to have a special communion with the island.
When "Christian" referred to "my son", he was not referring to Jack, but to someone else entirely.
Jack was lying in a bamboo forest and Vincent went to wake him up.
Maybe we should go back to the Purgatory-like theory. Even if the producers had confirmed that they are NOT in Purgatory, that doesn't mean that they could be dead or in a similar state (trapped, freezed, etc.)
Vincent is able to communicate with the island in all its forms and manifestations (Christian, Yemi, Dave, Walt, the Monster, Jacob, etc.)
Christian is a projection of Jack's mind: he uses the figure of his dead father to engage his line of duty, that is being a doctor. This mind's ghost even know about Jack's location: that's because Jack itself knows where he is, because he's not totally passed off or because he moved there after the crash.
The Island brought Christian back to life, just as it restored Locke's ability to walk and cured Rose's cancer.
This is possible because Christian was dead for only a day or two, so when the plane entered the Island's atmosphere (his blood wouldn't have dried up and his organs would still be operable (transplants etc.), and the Island got his blood pumping again, thus bringing him back to life.
But then why is he so composed and focused on a goal? If I had been dead for a few days, and then reanimated on a strange island, I would not be acting that cool.
Because like Locke he realizes the Island has great power because it healed him, and perhaps it spoke to him.
Being dead for more than ten minutes is enough to destroy the brain beyond repair. This is why stroke victims must get medical help immediately, as the brain stops receiving oxygen. Unless the Island can repair damaged brains too, which would be tremendous, but it did repair the nerves in Locke's back since it let him walk again.
When we see him in Jacob's cabin he doesn't look dead.
Christian took a drug (like that given to Juliet on the sub) to make him appear dead. His "death" was a setup to get Jack to take the flight he did back to LA. Christian woke up on the island, knowing exactly where he'd be.
That's a pretty strong risk, as 1) there's no way to be sure he'd survive the crash at all and 2) he'd risk medical examiners killing him in an autopsy or running out of air in a body bag, the morgue chamber or inside the coffin.
Could be worth the risk though if the work is important and the Medusa spider on the Island would be capable of making him appear dead, provides a link between the Island and Christian.
The coroner told Jack that Christian had a very high alcohol content, likely causing myorcardial infarction.
The coroner could have been in on it, convincing Jack and preventing real harm to the unconscious Christian.
Vincent is hallucinating.
Christian is a ghost, appearing to exert his influence in order to achieve his (as-yet) unknown goals. Much in the same way that Charlie's ghost managed to communicate with Hurley.
This mobisode is the on-island flash-forward alluded to by Damon in an interview with UGO.com It takes place after the flash-forwards we have seen in proper episodes and signifies Jack returning to the island by becoming unstuck in time much like Desmond in The Constant. Jack's future consciousness has taken over his body just after the crash so he can set things right. This would explain why the timing of Jack waking up is slightly different than in the Pilot. It would also tie into the theorized Stephen King connections, paralleling the ending to King's Dark Tower series. The ending to Via Domus is similar to this theory. Although the game is not in canon to the story, it had the blessing of the producers so one can assume it is conceptually canonical.
Christian crashed the plane himself, maybe in conjunction with the monster.
Highly unlikely, as the accepted theory is that Desmond's failure to press the button caused the plane crash. Damon and Carlton confirm that this is the definitive reason in their 'The Answers are Here' episode
Vincent could have an ability to see the dead. As others have pointed out, Christian seems much more human here than he does during all his other appearances, when he is possessed by the Man in Black. This makes it likely that he is appearing as himself. Going out on a limb, this could explain some other things Vincent does, like leading Shannon to Boone's grave in 'Abandoned' - Boone could have asked him to keep her there so she wouldn't go into the danger in the jungle.