I seem to recall reading an analysis of the (original) Alcubierre warp drive in terms of causality. Can you get the classical special relativity causality paradoxes which normally flow from FTL travel? There is some discussion of this at http://www.physics.purdue.edu/~hinson/ftl/html/FTL_part4.html#sec:stmanipulation
When we were talking about wormholes and causality, one of the ideas floating around was that virtual particles could enter a closed timelike loop and end up amplifying themselves each pass around, which took place outside of time. The effect was an instantaneous, spontaneously created spear of energy which would collapse the wormhole. I wonder if a similar phenomenon wouldn't occur with any sort of FTL travel that violates causality.
Wormholes have some properties in common with the Alcubierre warp, namely the need for negative energy, and the possibility of FTL travel and associated paradoxes.
More recently Anders referred us to http://xxx.lanl.gov/abs/gr-qc/9903061 which seems to prove that wormholes can't exist.
One of the papers referenced by Van Den Broeck is available at http://www.ioppublishing.com/PEL/article/cq14011l1/full/:
The expectation value of the stress - energy tensor of a free conformally invariant scalar field is computed in a two-dimensional reduction of the Alcubierre `warp-drive' spacetime. Unless the spacetime is in the Hartle - Hawking state at an appropriate temperature, the stress - energy diverges on past and future event horizons which form when the apparent velocity of the spaceship exceeds the speed of light. The likelihood of the spacetime being in this state, whether due to natural evolution or the application of technology, is briefly discussed.
This sounds a bit similar to the wormhole collapse phenomenon, although the author indicates that it might perhaps be avoided with some care.