There is some science at play (ie most folk can see differences but are not so good at absolute colour) BUT I am amazed in the 100 or so tweets I scanned no one have mentioned the Colour Temperature of Light and/or White Balance. The original image looks ok but it has a slight blue tint and the highlights in the background are “blown out” (in photoshop jargon “clipped”). What you see depends on whether you use this clipped background as your reference white our interpret the dress background as white. I have seen the mauve/blue cast in shadows on images where the highlights are blown out many times and I reach for the White Balance (see below) but so many people are used to just looking at their (often tiny) screens in a variety of lights and screen intensities and probably desensitized to what is colour balanced and what is not.
Hopefully most photographers will notice this straight away. And fix the cast before it is published. If you don’t believe me try colour balance for yourself, you can get a copy of the image here. download it and look at it with your normal software (I’m using Picasa here and the white balance correction tool here is call Neutral Colour Picker. You click on the eyedropper and then pick a white or gray part of the image click on that and picasa then removes any colour cast. If I click on the base colour of dress notice it was warmed (added a yellow/brown cast to the background).
Different software has different ways to do this and for example lightroom has the neutral tool eyedropper but it also an Auto White Balance button which is pretty reliable. A better place to start is in your camera. Get out your camera manual and work through colour temperature and white balance. Try out some of the setting and situations they are recommended. You will probably reach the same conclusion most other photographers have, set your camera to auto white balance and try to ensure the exposure is fine (no blown out highlights) Unless you think you need to do differently (ie you are shooting in a specific lighting condition with specific colour temperatures)