You are completely wrong on the first two,

An awful lot of CO2 (and other pollutants) are produced building nuclear power stations.

The energy from nuclear power is only cheap because it is heavily government subsidised and the clean-up is not included in costings.

As for the last point would you trust big businesses and governments to handle things properly when they could save money by not.

Aside from all that, Uranium mining is very environmentally damaging and it will run out eventually... not all that long if you run the whole world on nuclear.

Also if you 'go nuclear' to solve the world's environmental problems you would have to let every country have nuclear technology, and I'm not naive enough to assume that no one will try to misuse that technology.