Question: Is it scientifically correct to call Diamond an element? Carbon has a wide range of allotropes, so would it be correct to actually just call graphite, diamond etc an element. For that matter, could we call any molecule containing only one type of atom, an element?

Answer: 
The IUPAC definition of element is as follows:

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> A pure chemical substance composed of atoms with the same number of protons in the atomic nucleus. [IUPAC Goldbook definition of element](https://goldbook.iupac.org/terms/view/C01022)
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This seems to allow diamond to be called an element. But it's not a good idea, scientifically or linguistically, since it doesn't make sense.

Carbon is an element. Diamond is a *form* that the element carbon can take.

Let me give you a car analogy:
Toyota is a brand of car. The Camry is one example of a type of Toyota car. I.e., it is one form a Toyota can take. That does not make "Camry" a brand of car, nor would it make sense to call a Camry a car brand.

In summary, referring to diamond as an element, rather than a form an element can take, is like referring to Camry as a car brand, rather than as one of the brand's models.
Diamond is a form of *pure carbon* (which is an element). Logic may lead you to believe that diamond is, therefore, an element. However, this is a bit circular because if you say that diamond is an element, then every allotrope of every element also falls under the same consideration. 

Also, in order for diamond to be a unique element, the molecules that make it up should have a different number of protons than any other element on the periodic table. Since a diamond is made of carbon, it is really just another form of carbon.