Apparently CTCs violate no-cloning: http://arxiv.org/abs/1008.0221 This seems like a big deal to me, since it shows a foundational conflict between general relativity (which generically permits CTCs, although perhaps they don't exist in our universe) and quantum mechanics (since without the no-cloning theorem you can presumably circumvent the Heisenberg uncertainty principle). My skills aren't up to understanding the paper in depth. However, the result sort of seems plausible to me. A CTC is basically a time machine, so it seems like it would allow you to measure a particle's position, then go back in time and measure its momentum before it had been perturbed by the position measurement. Since I'm not an expert in this field, I can't judge whether the result is really reliable and model-independent.