... blue and brown. Just now, I opened the Washington Post link on my 24" screen in a sunlit room, and it was clearly white and gold.
Though the sensations are vastly different, brown is really dark yellow. The underlying color of that part of this dress seems to be very near the perceptual boundary (probably just on the yellow side of it). This picture seems to have the dress in a non-obvious shadow, so when it is viewed by someone whose visual system doesn't adequately pick up the shadowing and compensate, it crosses the boundary and appears light brown rather than dark yellow.
Another perceptual oddity is that a very slight bluish tinge to white makes it appear "whiter than white", especially in sunlight or other strong lighting. (I suspect this works by mimicing the differential response of the various color sensors in the eye when exposed to very bright light, though blue may also "cancel out" a bit of the yellowing of aging cloth.) Laundry products up through the 1950s or so included "bluing", a mild blue dye for producing the effect. (It fell out of use when it was replaced by a fluorescent dye that reradated energy from ultraviolet as blue, making the cloth literally "brighter than white" {where "white" is defined as diffuse reflection of 100% of the incoming light}, and which, if mixed with detergent products, would stick to the cloth while the surficant was rinsed away.) I suspect some of the "blueish is brighter" effect is going on here.
When I view the picture straight-on on my LCD display, the light cloth on the upper part of the dress appears about white and the image appears somewhat washed out. Meanwhile the lower half has a bluish tinge. So I suspect the cloth is actually nearly-white with a bit of blue. (Viewed off-axis it's very blue, but the other colors are over-saturated and/or otherwise visibly off-color. So off-axis viewing makes it look more blue and this probably adds to the controversy.)
Another color-perception issue is "teal", a color between blue and green. There are paint formulations of this color that give the sensation of "distinctly blue with a greenish tinge" to some people and "distinctly green with a bluish tinge" to others, even under the same lighting and viewed from the same angle. (I'm in the "slightly-bluish-green" camp.)
The first place I encountered this was on the guitar of the filksinger Clif Flint. (On which he played _Unreality Warp_: "... I'm being followed by maroon shadows ..." B-) ) Apparently his fans occasionally had arguments about whether his guitar was blue or green, so he sometimes headed this off (or started it off on a more friendly levl) by commenting on the effect.