This was before Citizen's United by the way. It is eye-catching to read that American Electric Power literally bought the town it was polluting for $20 million. Residents had had enough with the local coal power plant when it started expelling blue smoke on occasion. This is an interesting real-world application of the Coase theorem. After likely causing permanent damage to the livelihoods and health of the residents of Chesire, Ohio, the utility literally kicked them out, payed them handsomely, and made them promise never to sue.
The people got about three times the original value of their homes ($150,000 per home). Some thought that it was a good deal, while a minority thought that the company got off easy. The utility was certainly a lot better off than it would have been had it been sued for health damages.
The power plants in questions actually had been cleaned up significantly to meet environmental standards, but still posed a health hazard. A large part of the reason is that it still used high-sulfur coal, which is much cheaper (but dirtier) than the alternative. Rather than fight a legal battle the town agreed to (literally) sell out to the utility. This probably left everyone better off (except lawyers) than if a legal battle had ensued.
While this is a case that no doubt validates the premise of the Coase theorem, it is a rarity that companies and citizens will come to an agreement like this. In fact, this was the largest deal of the sort ever, with 221 people involved. Most cases involving unwanted externalities involve many more people and companies that might be willing to go through litigation and fight it. So while it may be ideal to spur regulations and taxes for bargaining, it is usually not practical aside from a few small, local cases. It certainly will not happen with something as big as climate change. I fear that establishing property rights will just lead to more conflict and more lawsuits. Like many economic theories, the Coase theorem is idealistic and works in a vacuum, but the right conditions for it to be beneficial are too rare for it to make much of a difference.