Does special theory of relativity limit velocity to speed of light, but general theory not? In fact I don't even need to spin around, just being on the spinning earth is good enough. 
Suppose I look out into space at the nearest star, Alpha Centauri, approximately 4 light years away. Working from the gravity accelerated frame of reference that I occupy on the surface of the earth, th star appears to go around the earth in one day, travelling a distance of $2*\pi*4$ or roughly 24 light years - in a day.
What I am really getting at, is that relativity tells us all frames of reference are valid, as well as that things cannot travel faster than light. But from this particular frame of reference, that would not seem to be true.
This accelerated, rotating frame of reference can be described as equivalent to some other frame by general relativity, so I think it is valid to look at it from different frames of reference.
Does this imply that the theory of general relativity does not place an upper bound of the speed of light on velocity?
 A: All non-accelerating non-rotating frames of reference are equal, so that straight away explains the apparent violation. 
In general, apparent motion can easily exceed the speed of light. For instance, if I'd shine a laser on the moon, I could make that spot move over the lunar surface quite quickly simply by rotating the laser here on earth. If I rotate the laser fast enough, the spot will in fact move faster than the speed of light. This is possible because that laser light spot isn't a physical object; it's the effect of the lasers photons being reflected. And as I rotate the laser, the photons leave earth in different directions. The spot that I see move therefore consists of reflected photons, bu those are different photons over time. Each individual photon is still bound by the speed of light. 
A: General Relativity is build such that it reduces to special relativity locally. That means that if you perform an experiment locally no particle or wave can exceed the speed of light. As you have pointed out, globally this is no longer true. For example in inflation, spacetime is created at such as speed that spacetime points that were initially causally connected are no longer connected - they must have receded at a speed larger than the speed of light. (By the way, this is one way to resolve the horizon problem).
In principle this is not surprising if you have already heard about cosmology. The 'recessional speed' of galaxies is proportional to their distance, and thus, at some distance their speed exceeds the speed of light. To be a bit more precise (and this is way I wrote 'speed' in quotation marks): Keep in mind that velocity can be only compared locally in General Relativity, since it is a curved manifold. There is no unique way to compare velocities of two objects that are not at the same spacetime point. (There is the standard example of parallel transport on a sphere).
