If there is a leak of nuclear material into some form of medium that allows for it's wide dispersal into the environment, then you're likely to start coming across animals of a stranger nature in about one or two generations...
And when you think about the human body, it's remarkbaly like a computer. It's a very complex thing on the surface, but it's actually a very simply thing under scrutiny. It's ones and zeros arranged in very clever ways to offer up the functionality that exists today... (on a very basic level at least)
When you start messing with this basic coding things start to go crazy. Some things just don't work and the device simply won't function in any appreciative way, but some perversions of the norm do work. I think it could be the same for living beings. Something about radioactive exposure screws with the normal coding of biological forms and leads to weird but viable perversions.
At one point this is sickly and heinous and one technically wants to either stop this or mitigate this appalling thing. But...from another angle...one realizes that life is...tweakable. That you can change things here and there and end up with a new result. We were already doing this with breeding, started doing it with chemicals, we could probably even do it with certain kinds of sound waves, but the basic thing is that we are coming up on a time when greater and greater understanding and methods of the tweak allows us to manipulate the fundamental character of nature- perhaps any detail in it.
I won't even waste my breath talking about the dangers and evils of blah, blah, blah, because living this long I realize that if it can be done, it will be done, regardless if it is illegal or immoral. And it will be accepted if it has a convincing enough hype surrounding it. And there are going to be an array of positive benefits to this- not to mention vain ones. Imagine if you could decide on your eye color...or your childs. You know how long people spend customizing the look of their avatars in various virtual games and social forums and such. It's like clothing, we always feel the need to modify our look. Similarly, if we could modify the world and all that's in it, I think people would do this constantly. You can end up with Teenage Mutant Ninja Turtles or Godzilla. You can engineer human beings that can survive on Mars or other off-world environments.
Well...enjoy the future. You have no other choice