Whenever I see footage of US troops I notice they have an american flag patch on their shoulders, that is reversed…stars on the right. A google search gave me this page:
http://www.newmexicosdf.org/drumrol2.htm
It implies its just a mistake-“If you are wondering why the Reverse Flag it is simple. A Government Contractor making these for our forces in Iraq made a MISTAKE and did them backwards. We of course, and all the rest of the U.S. Forces get to live with it, forever. Enjoy!”. Anyone know if this is true?
It’s not a mistake:
http://boards.straightdope.com/sdmb/showthread.php?t=175734&highlight=backwards+flag+uniform
Has links to the other times this has been discussed, but Chronos’ has a great, simple answer:
Of course as someone did in the thread where I quoted that answer, I’ll also clarify that for any nitpickers and say that this applies only to depictions of flags (decals, patches, etc) and not actual flags themselves, which of course, fly free.
The guy in that link clearly has no clue what he’s talking about, unless he was joking. US military personell have been wearing backwards flags on their right shoulders for a very long time.
Oh well. I suppose that’s why he’s in the New Mexico state militia instead of the real military. 
The reason that Chronos gave is correct. In the Air Force we don’t wear flags on your BDUs or our DCUs, but we do on our flight suits, on the left shoulder. That results in the orientation of the flag that you’d expect to see, with the field to the upper left. If we wore them on the right shoulder the field would be on the upper right like the Army.
On a TV show one time I heard it explained by some general that if the flag was oriented the way you’d expect, it would imply going backwards, namely retreat. They don’t want to imply we’d retreat, so the flags fly as if going forward…
What people tend to forget is that the (actual) flag does not have a “left” and a “right”, it has a hoist (to the side that attaches to the flagpole lanyard) and a fly (to the side that flaps in the wind). The union (the starfield) is located at the upper hoist corner. And when the flag is in motion, or a representation of it is portrayed as if in motion, it goes hoist forward, whatever direction “forward” is.