What happens if Kate Middleton's baby turns out retarded?

No, he can’t. Nothing in the Act of Settlement confines the succession to those who agree to it.

Until recently he could take himself out of the line of succession by marrying a Catholic, but that tactic is no longer effective.

Each country has its own succession law. Monegasque succession law allows adopted children to inherit the throne, and in fact this has happened in the past. But UK law, currently, does not.

A thing that he couldn’t decide to do if he were actually king, since according to the fundamental laws of the kingdom, the king of France couldn’t dispose of the crown or change the order of succession.

But since his own claim rests on the validity of such a decision by his ancestor Louis XIV (excluding from the succession the Spanish branch of the Bourbons) I assume he would dispute that.

so what is the final answer to the original question then? that if prince george turns out retarded, only an act or parliament can remove him from the line of succession? and they don’t have to if they don’t want to? then what

Nothing in the Act has to. The common law has always provided for the renunciation of titles and bequests.

Not quite. You couldn’t renounce a peerage until 1963, and that only applies to hereditary peerages. And the title is only disclaimed for the present bearer, not their heirs.

Only an Act of Parliament can remove him from the Succession, subject to another 15 Acts of Parliament being passed in the other Commonwealth Realms. A far easier method however would be to declare him incapable of office under the Regency Acts and have a Regent appointed to conduct the office’s duties for him.

who declares him incapable? and who decides who does the declaring?

Wikipedia:

Oh no! There’s a vacuum at the center of power!

ctnguy answered that clearly and succinctly in post #9.