There's been some debate about distortions in the CMB radiation that coincide with the movement of the solar system through the galaxy. Here:
http://www.astronomy.com/ASY/default...=a&id=2640
I think a rebuttal to this is that it may have been a statistical fluke, i.e. the CMB radiation happens to have fluctuations that coincide with the motion of the solar system. It seems fairly illogical to me.
But I wonder, would it be possible to test this? What if you put a space probe in a fairly far orbit around the sun, and then took a picture on one side of the sun, and then a second on the other side. Would the speed be enough to make a measurable difference?