Will the NY Times and others now apologise to the Pope and the CDF ?

I do not think they will. But they should in regard to their stories about the Lawrence Murphy case.

I wonder if the BBC or The Times and The Sunday Times will too?

See

Smoking Gun Memo In Murphy Paedophilia Case!

The Murphy Case: What Really Happened inside the CDF

Computer mistranslation of key Vatican memo undercuts media criticism of Pope