---Spoiler Alert---
To me the movie centered around the idea of the profound effects of a single choice can have. In 1849, when Adam Ewing saved the stowaway slave, it set into motion of events that eventually saved the human race from extinction 500 years later.
In detail:
Adam Ewing saved the slave which resulted in saving his own life and publishing the journal.
The journal inspired Robert Frobisher to create the Cloud Atlas Sextet and subsequently kill himself upon its completion.
Letters from his lover, Frobisher, inspired Sixsmith to give the report on the power plant to Luissa Rey.
The story of Luisa Rey, inspired her neighbor, Javier, to write a story about her, that the publisher, Timothy Cavendish, read. It inspired him to escape from the retirement home, although the book drew a tighter connection than the movie.
Timothy Cavendish's experiences were made into a movie that Sonmi 451 watched. It inspired her to rebel against the corpocratic government.
Her and her words became a religion to the tribesman, Zachary, 106 years after the fall. It inspired him to help Meronym. Meronym's goals were different in the film, than in the movie. In the film, she uses a transmitter from the top of Mauna Kea to summon help because the earth is dying.
It ends with the two of them decades later telling the story around a campfire on an alien planet, which would not have been possible if it was not for the single act of kindness Adam Ewing showed by saving the slave in 1849.
Edit:
@Lesley, the movie hinted that the actors were basically playing reincarnations of themselves over time, but it only hinted at it.
The book hinted at it a little more strongly suggesting the reincarnations were Henry Goose>>Robert Frobisher>>Luisa Rey>>Dermot Hoggins>>Timothy Cavendish>>Sonmi 451>>Meronym.
The idea is that over the lifetime of the soul, it gradually transitions from the Murderous Dr. Goose to the wise Meronym.
What about the birth marks?