Hey thought I'd chip in on this one.
I'm a sports podiatrist based in north Island NZ.
Firstly this article linked
www.painscience.com/articles/orthotics.php is really a load of bollocks. As a podiatrist we spend 3-4 years at uni studying anatomy, physiology, biomechanics etc as well as material science and the fabrication of orthtoics.
Unfortunately orthotics have in the past been over sold by both podiatrists and physiotherapists hence why I think they have a dodgy reputation.
Firstly do they work...that depends wholly on whats wrong with the individual, there is a strong body of evidence indicating the use of orthtoics for a number of lower limb complaints. Conversely there is evidence contraindicating orthtoic therapy for other complaints
Will they "correct" none problematic flat feet...no of course not, nothing short of major reconstructive surgery can do that.
Interestingly enough if you ask how they work...well to be honest no one has a clue at the moment. a lot of the traditional ideas have been proved wrong. There is however a huge amount of ongoing research conducted in the hope of increasing patient outcomes who use orthtoics.
My advice seek a good podiatrist if you have painful feet or legs, combine that with a good physio I find that works in most cases