Will quickly switching polarity on a peltier damage it?
There is plenty of info on the web regarding this subject. The biggest problem is fast rise time as a pletier acts as a voltage source. Last time I checked its bad to plug in power supplies backwards. Rate limit any control signal into a peltier and avoid switching it from postive to negative instantly. 

I can't speak for the time because it is application specific and device specific. I've seen a half to 1 second to wait in some applications for the peltier to 'settle' and reduce the delta-T across the device before switching polarity. In your application this could also be accomplished by zeroing out the PID before and after switching or a relay before the DPDT. Some applications use an inductor to limit inrush current.