In fact in many ways it set back the dreams of UI by teaching a generation to value nonsensical interactions and poor ergonomics over usability
I'd checkout John Underkoffler's Ted Talk: http://www.ted.com/talks/john_underkoffler_drive_3d_data_wit...
That itself ain't bad. Star Trek: The Next Generation pretty much introduced the world to the concept of touchscreens, back in the time when they pretty much didn't exist.
Also, somehow the "internally incoherent" movie UIs still feel order of magnitude better than what we use in the real world, especially on mobile, which is mostly a mess of crappy and incoherent design.
Star Trek interfaces set the gold standard for realistic UI, while Minority Report was not a UI anyone would ever want nor even should aspire to create.
Footnote: Oddly enough the consultant on the interface for Minority report was Jaron Lanier, who I respect immensely for his technology theory -- just not his designs.
I wholeheartedly agree with your evaluation of LCARS. That's why I still keep sketching out LCARS-equivalents of UIs for existing devices (it's actually quite hard to do right; you can't go there half-way - LCARS mixed with non-LCARS elements looks like crap) and want all my home automation to be run by one :).
Another thing Okuda was a master at was logos and insignia. They set a quality standard that is very rarely met in the real world.
Exactly why people are influenced by it.
Anyone who has ever worked with any kind of media editor knows that "waving your arms in the air" is about the least desirable imaginable interface for such.
The only difference is that John Anderton seems to be able to get his software to do the stuff he wants it to do.