I am a huge fan of Fringe, which is similar in many ways to STID, and is a show created and created by the same creative minds (Abrams, Orci, and Kurzman).
My favorite Trek is DS9, but I am very much enjoying the latest film franchise.
Following are some thoughts that contain spoilers for both Fringe and STID.
Fringe is a show about (among other things) two alternate Earths coming into contact.
The Earths are subtly different, and the show LOVES to show scenes from subtly different angles.
For example, in one episode, a father on Earth One is shown teaching a coin trick to his son, who is terminally ill.
On Earth Two, we see the same boy, still terminally ill, who is being taught the same coin trick but by his mother.
We also see that in Earth One, the twin towers were destroyed on 9/11 while on Earth Two, the twin towers were saved, but the Pentagon and White House were destroyed.
Even seemingly insignificant details are shown to be different, such as Back to the Future starring Eric Stoltz, rather than Michael J. Fox.
So for those who think a lot of the subtle differences in, for example, the Engine Room scene of STID are just tugging on nostalgia (or- more unkindly, laziness or a lack of creativity), I would strongly disagree.
The subtle differences of a parallel reality are clearly an idea that interested the creative team in 2009. To my mind, it's a great idea and one of my favorite things about this new incarnation of our favorite franchise.