The evolution of mermaids is in fact impossible no matter how you look at it.
As fish evolving human characters or a hominid evolving fish characters. Neither of these things are possible.
Believe me or not, but it can all be found in this book. http://www.amazon.co.uk/Evolution-Douglas-Futuyma/dp/0878932232/ref=sr_1_5?ie=UTF8&qid=1369913401&sr=8-5&keywords=evolution
It's a myth and honestly I think How I Met Your Mother actually explained a more viable hypothesis to the origin of them than anyone in this thread.
Now you might say that you should be careful about debunking myths because because of the discovery of such creatures as giant octopus and squids confirming a lot of the old stories. It should also be mentioned that the sea serpent stories are believed to be early discoveries of a giant herring. If only it had phycoerythin pigments... (cookie to the first one to get this one)
thaluikhain said:
You'll also note that sea mammals like whales and dolphins don't have gills, they breathe air same as we do. Evolving gills evidently is no small thing.
Actually, there's a hypothesis claiming that for us to evolve gills is impossible. The hypothesis states that a if a complex structure is removed through evolution it can never come back through further evolution. I can't remember the name of the hypothesis though. I just wanted to add to what you said, what you said was quite good as it was.