Have people actually been shown a real photograph of this dress, i.e. an image that's not shown at the screen?
Look at your screen from beneath. Or if you have a laptop, turn the screen as far as possible away from you so that the angle between a line from your eye and the picture becomes very small. You can try it with this page. The blue on the top changes to a greenish color, and also other colors change. Anyhow, when you do this you'll see the color of the dress change from black and blue to white and gold. So the problem is related to looking at a (LED) screen from different angles. Black turns to white (grey, actually) and blue to gold.
For example, look at this photograph:
Now, look at it from beneath. What do you see?
Or look at an arbitrary picture somewhere on the web. You'll see the same effect.
I think that if the real picture of the dress (so not the picture on a screen) is shown to a number of people, all will perceive the dress as black and blue.
So: print the picture, show it to whoever you want, and see how they perceive the colors of the picture. It's my guess that the described phenomenon won't be there. All people will see the colors of the dress (in the same conditions or context) in the same way!
It was just a fake internet hype!