Most of the theories posted here after the finale try to sum up the meaning of the show. I'm not going to do that. Instead I'm going to try to tackle the many unanswered questions and dangling threads that Damon & Carlton had left to our imagination. So here goes, in no particular order:
Q1:
Who shot at Juliet, Miles, Sawyer, Charlotte, Locke & Daniel in the outrigger in "The Little Prince" AND how did the other survivors of Ajira 316 die?
A1:
After the death of Jacob, the Man in Black disguised as Locke hits Richard Alpert in the throat and carries him off on his shoulders. He brings him to one of the outriggers and smacks him in the head until he's conscious again. They take the outrigger towards Hydra Island when Locke notices another outrigger in front of them. Since Sawyer is one of the candidates, he shoots at him trying not to hit the real Locke, who he still needs to complete his loophole. Juliet shoots back and hits Richard. Richard being immortal is knocked off the boat, but is unharmed. The other outrigger vanishes into thin air. The Man in Black pulls Richard back into the outrigger and they make it to Hydra Island. The Man in Black reminds Richard that he asked him to dispatch the other survivors of Ajira 316. Richard asks why and MIB explains how he wants to leave the island and they stand in the way of MIB taking Ajira and leaving the island. Richard refuses to help kill them, so MIB turns into smoke and kills them all right in front of Richard who can do nothing to stop him. Then he knocks Richard out and brings the outrigger back to the main island, where he ties Richard to a tree.
Q2:
What is the significance of Walt's powers, how did he get them, and why does Vincent seem to be a catalyst for important events?
A2:
While living in Australia, one day Walt's stepfather Brian Porter brings home a business associate to meet the family, his name is Jacob. Jacob shakes Walt's hand and pets Vincent. Jacob and Walt are talking while Susan & Brian are in the other room. Jacob asks Walt why he looks so sad. Walt says he doesn't have many friends in Australia. Jacob says that it's easy to make friends, all you have to do is talk to people and introduce yourself. Walt says that he's afraid, but Jacob says, don't worry, you have a magnetic personality.
In a nutshell, Walt's powers are the ability to bring individuals together (summoning birds, polar bears, Vincent, and most ironically the Others on their boat which eventually led to his capture). He can communicate telepathically (when he told John not to open it), he can astrally project his image to other people's minds (to Shannon, Sayid & Locke), he reads other people's minds in both reality and in dreams(when he dreamed of Locke in a suit and everyone was trying to hurt him), and he has the power of telekenisis (his knife throwing skills and quite possibly the burning of the first raft).
Vincent has also proven to be special. As he was also touched by Jacob, Vincent has shown the ability to show up when most needed by someone as a catalyst. He was there when Jack woke up on the island and needed to save the survivors of the plane wreckage. He brought Charlie the virgin Mary statue, when Charlie needed to reassess his heroin addiction (also in the process he showed him where Sawyer's supply stash was). He brought Hurley the arm of Roger Linus when Hurley needed to discover the Dharma van. He's the one who most likely found Desmond in the well before Bernard pulled him out. And he settled down next to Jack so he wouldn't die alone.
Vincent was special just as Walt was special. Jacob made a spiritual connection between the boy and the dog, so that even when Vincent and Walt were apart, Walt could be with the people he cared about and help them, through the vessel of the dog.
Q3:
Why did Ben let himself get captured by Rousseau in the net?
A3:
Ben wasn't lying when he said that he was coming for John Locke. Ben was handed one of Jacob's lists and on it were the names of the candidates he needed to mind-screw in order to set off the next domino in Jacob's plan. Jacob wanted John to stop pressing the button, because he needed Desmond to be exposed to the electromagnetic energy from turning the failsafe key. So Ben was there pretending to be Henry Gale to get Locke to lose faith in the button.
Q4:
Why did Ben have Sayid kill people off the island and what was the significance of Sayid shooting Ben as a child?
A4:
Sayid's purpose on the island was to groom Ben to fulfill his destiny to be Hurley's second-in-command. Everything that happened needed to happen in order for Ben to become the person he was supposed to be. So Ben was supposed to get shot as a child by Sayid in order to get "reborn" as an Other by Richard in the temple. He lost his innocence and became the Ben would could be capable of the things we've seen Ben be capable of.
In order for Sayid to shoot Ben, Sayid needed to be groomed as well. He was not in fact a killer before he came to the island, but merely a torturer. He needed to lose Nadia (which we saw Jacob have a part in) and he needed someone to blame (Widmore and his men). So Ben killed two birds with one stone, he got his revenge on Widmore by having Sayid kill all his men off the island, as well as grooming Sayid to become a seasoned killer, one who would hate Ben enough to kill him as a boy.
Q5:
Who ordered the purge of the Dharma Initiative?
A5:
Charles Widmore taking orders from Jacob. Charles was the leader of the Others at the time of the purge not Ben. This was shown in "Dead is Dead" when Charles was exiled, the Others had already taken over the barracks. The reason Jacob ordered Charles to purge the DI was because they were about to cause more harm than good. The DI built the Tempest station and were going to use it on the Others as a test. As semi-explained in the Sri Lanka video of the Lost Experience (verified as canon by the producers) one of the purposes of the DI was the prevent the extinction of the human race by overpopulation. Humans are reaching their carrying capacity, too many people with too little resources. So the DI would kill a small percentage of the world's population, so that the majority of the world's population would not die out. They built the Tempest station on the island to experiment with the island's indigenous population and see if it would work before they did it on a global scale. Jacob got wind of this and ordered Charles to use their own weapon against them, thus purging the DI off the island.
Q6:
Why could pregnant women who conceived on the island, not give birth on the island?
A6:
Juliet told us that it was conception on the island, that led to the mother/child deaths. She asked Ben if she could bring a mother off the island to give birth and he said no, but we saw her theory come to fruition when Sun gave birth to Ji Yeon off the island (who had been conceived on the island).
The answer to this mystery is actually quite simple: radiation caused by Jughead. Ethan was conceived on the island by Horace & Amy and was born healthy before Jughead was detonated. Juliet set off Jughead and its energy negated the energy released by Radzinsky's drilling just as Faraday said it would. But this doesn't mean there weren't side effects. We know that Jughead in the 1950s was leaking radiation, killing several of the US military officers whose bodies Miles communicated with. So a child conceived on the island had too much radiation exposure and the fetus turned on the mother killing them both. When Sun was off the island, she was far enough from the radiation for there to be enough of an effect to kill both baby and child. This does not mean that Ji Yeon was not affected by the radiation, which most likely gave her Jacob-like powers.
Q7:
Christian told Jack in the church at the end that the sideways world was one that they all created together so that they could meet up before moving on. How did this world get created?
A7:
Jughead. Juliet set off Jughead which did indeed split the universe into two distinct timelines, one in which Flight 815 never crashed and the one which it did. Unfortunately the universe had to course correct itself because it would be impossible for one person to be simultaneously living in two distinct timelines. So in one timeline they're living and in the other timeline they're dead. They did create the sideways world all together. They all helped set off Jughead. And that's why Richard told Sun that he watched them all die. Because they did die. But they also lived too. Jughead created a Schrodinger's Cat scenario (too complicated to explain here, you can wiki it) where they were living and dead at the same time. This happened because in the sideways world time was non-existent. They all needed each other to move on, so their minds once they died latched onto this timeline created by Jughead so that they could all be together one last time.
Q8:
Who was in the cabin, if not Jacob?
A8:
I can't take credit for this particular theory, but I don't remember where I read it or who said it. And of course, I'm elaborating on the germ of this unknown person's idea.
The Man in Black was indeed the person in the cabin who said "Help Me" to John." So how could he also be Smokey terrorizing everyone on the island outside of the cabin? Well, when Ben turned the wheel, MIB flashed with everyone else. Then when they flashed back to 2004, that's how he could be in two places at once. Trapped in the cabin by the ash, and haunting the island as Smokey.
That also explains how Christian appeared to Locke in the wheel chamber back in the olden days.
Q9:
What was the significance of Aaron and why did Richard Malkin send Claire on Flight 815?
A9:
Malkin was an agent of Jacob. Claire needed to get to the island to help Jack and Kate and company influence the events which led to the destruction of the Man in Black and the saving of the island. Aaron was born on the island, which means that he now possesses the powers and energy of the island. But his destiny was not to live on the island, but in the real world. And the sole purpose of the Oceanic 6 leaving the island was to get Aaron back to society. Aaron is one of the saviors of humanity in the real world, just as Walt & Ji Yeon are. Children of the island who have powers but who are destined to help others in the rest of the world.
Q10:
Why did Radzinsky edit the Swan orientation film and why did he create the blast door map? Also, what were the circumstances behind his death?
A10:
As we saw in season 5 Radzinsky was a control freak who wanted to harness the powers of the island. When he ended up causing the incident, Radzinsky was consumed by guilt and made it his new life's purpose to fix the mistake he created. Jacob saw Radzinsky's situation as almost identical to the his mistake of killing his brother and causing the problem. So Jacob appeared to Radzinsky and informed him of the need to protect the candidates. Radzinsky edited the Swan orientation film to remove footage of time traveling Jack, Sawyer & co which would alert them to their own presence on the island in the 1970s, when they watched the films later on. He also created the blast door map, to help them and Desmond learn the geography of the island.
Inman was also an agent of Jacob who helped lure Sayid to the island. Shortly after leaving the military in the early 1990s, Inman joined the Dharma Initative (which unknown to him was already defunct) and was brought to the island by the Others. He went to work with Radzinsky (now an agent of Jacob too). They pushed the button together for a while until they got into a disagreement similar to that of Jacob and the Man in Black. The same disagreement that Charles & Ben had as well, that of the nature of man and if it was worth protecting. That led to Inman killing Radzinsky and later telling Desmond that it was a suicide.
There are more questions, such as the food drop and such, but I think I want to leave that to the DVD extras which promise to explain that as well as Ben & Hurley's time on the island after Jack's death.