Let me give a more detailed reasoning for my example earlier of effects that would be predicted by Setterfield but that fail to be seen.
We use of doppler effects to measure the rotation by looking at the different relative speeds of each side of the galaxy.
Now, if you assume that the galaxy is not rotating at relativistic speeds and you only consider the velocity vectors directly towards and away from you, the formula for doppler shift reduces to
(velocity of object)/(speed light) = (change in wavelength) / (wavelength)
(Barry has been very clear that it is frequency that changes with c.)
Now if you solve for the change in wavelength, you will see that it is inversely proportional to the speed of light. So if you take a given situation, plug though the change in wavelength with a higher speed of light to get the change in wavelength, then go back through with today's speed of light, you will see that your speed measured will be off by exactly how much the speed of light has changed. The exact same thing will happen if you use frequency instead of wavelength.
Take M31. It is about 2 million light years away so light would have been necessary to have been traveling at least a few thousand time faster when it left than now to get here in 6000 years. This means that the measured speeds of rotation are off by at least three orders of magnitude. And M31 is the nearest large galaxy. The problems get much worse at greater distances.
The rotational speed of M31, the largest nearby large spiral galaxy, has been measured at 275 km/s. (
http://helios.astro.lsa.umich.edu/Course/Labs/tully_fisher/tf_intro.html ) It is about 2 million light years away so let's take as a conservative (and one that makes the math easy) factor that light would have been traveling at 1000 times the current speed of light when it left Andromeda to get here by now. This means that the 275 km/s must also be multiplied by 1000 giving a speed of 275,000 km/s! This is over 90% of the speed of light! Imposssible for a variety of reasons.
Since there is not a sharp dropoff in measured rotational velocity as you look further into space, more distant galaxies would be in the position of having their stars orbiting at speeds greater than the speed of light! As it is, the measured velocites are higher than the visible matter would allow which is one of the reasons that dark matter is proposed to account for the extra mass that is needed.