whole

The only thing here I'd call incorrect or wrong is the absense of "of" in the whole of mankind.  Are we supposed to be talking about the redundancy?

I think the "repetition" is common, for emphasis, or style.  These uses may not be formal, and may be considered bad taste by some.

Throughout his whole entire life would really be redundant, but I believe it's common.  The objection is like saying it's incorrect to repeat a musical sequence more than three times.  How can you legislate style and taste?

I suppose the rule, if such there be, is that you shouldn't use two adjectives with the same meaning to modify one noun.  This is a very large huge problem.

In the case of "mankind," the word already means "all humans," so "all mankind" would be redundant. 

At first, scientists thought only XXXX people had this problem, but they have now learned that the whole of mankind has been afflicted.  I see nothing wrong with this.  "Mankind" alone, would not work.

I wouldn't say it is common, and where it happens, it tends to be in set combinations.

a large huge problem sounds very odd as it isn't using a standard combination.

A great big problem sounds fine as 'great big' is a standard combination.

Um...I'm trying to think of some futher examples beyond 'great big' but none come to mind right now. Oh, 'tiny little' is another standard combination. I really can't think of any others...