Comments below regard both Divergent and Insurgent.
SPOILER ALERT


I did not read the books.
I liked the movies even if they are similar in theme to the Hunger Games.

However after watching the movies I got to thinking about some of the details. I came up with a few nits and NANJAOs.

Divergent:
After the test, the person can choose any faction.
I assume that some of the Faction-less were people who choose the wrong faction and could not fit in.
Why they can't try another faction seems wrong.

When the group first went to Dauntless, I found it odd that no Dauntless born person volunteered to jump first.
I also found it odd that the Dauntless area didn't have any evidence of families.

It was sure a coincidence that as soon as Tris passed to be official Dauntless, that they get controlled to wipe out her old family.

Insurgent:
A new device has been quickly invented to reveal someone's faction. But what if someone choose a different faction from what the original test suggested?

I'm trying to wrap my head around the facts revealed when the mysterious object was opened by Tris. Hundreds of years ago something bad happened to the world. Instead of all survivors working together, an experiment was set up where the faction system was enclosed inside a wall. But it was hoped that Divergents would eventually emerge. However no one actually knew about this, so Divergents became something to be feared would break the peace. The truth was sealed in the object that only a true Divergent could open. Anyone else who tried died in the process.
Smart thinking. NOT!

Allegiant:
I have not read the books, but I understand this movie diverges from the source (pun intended).
This movie helped answer a few questions but created more as well.
At the end of Insurgent, only a pure Divergent could open the box.
We find out that there is, indeed, still a society outside the wall that is using the population of Chicago as an experiment. The birth of a Divergent is considered progress.
In addition to this society, Tris discovers there is a group of fringe dwellers from which her mother came. I thought her mom was raised Dauntless. For some reason the fringers never tried to get into Chicago. We further discover that the society kidnaps kids from the fringe and erase their memories. But the mom had her memory from the fringe stored. Also the mom was willing to help Dave, the director of the society, with the Chicago experiment. Did she know the whole story?
I was also confused as to why those left in Chicago were willing to kill each other. The only motive I saw was that one group was against the death penalty.