The flash sideways gave us the following...
- Sawyer, whether criminal or cop, will always want to hunt down the man who killed his parents - this reinforces the idea of the universe course-correcting itself, and causes us to wonder just how much influence that Jacob's touch has on the future events of someone's life. This further reinforces the theory that the two timelines may converge at one point.
- Miles' dad, Pierre Chang is ALIVE in the flash-sideways and working at a museum with Charlotte. This is important as it provides more clues as to when the split between the timelines may have occured (after the incident?) and that Dharma people who were on the Island at the time of the Incident were able to make it off the Island at some point after the split (Ben, Roger, Pierre, Ethan).
- Miles' life isn't quite so screwed up in the Sideways world, possibly because he has a father-figure. This is one more example of the existence of the Island screwing up people's lives.
I thought these were good pieces of the story that we got out of the Sideways story, to name a few.