I agree that natural selection would probably remove organisms with "half-formed organs". Would you have survived if you were born with half a heart? That is NOT what the TOE predicts, rather small, incremental changes that still leave a fully functioning organ but one that may be better able to do its job in some way. Generations of small changes CAN add up to large changes.
I don't see that your link was to a non-biased site. It makes many false statements and strawman arguments. It also used quotes by SJ Gould. He is discussing punk-eek, punctuated equilibrium. He never meant his theory as an over-throw of evolution. It is more of a way of describing how changes can happen "relatively" quickly given a large change in environment and selective pressure. One of the biologist can explain this better than I can, and hopefully correct my errors.
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Asgara
"An unexamined life is not worth living" Socrates via Plato