Coordination in "both...and"

The important thing is that both coordinated tokens should coordinate to each other, and to the following expression which they are modifying.

In this case, in singular form:

often have a mass form
often have a count form

you can now use the construction both ... and ...:

often have both a mass form and a count form

or the better, avoiding redundancy (the version that was used in your book):

often have both a mass and a count form

Now the plural form:

often have mass forms
often have count forms

Using the both ... and ... expression:

often have both count forms and mass forms

or, again, avoiding redundancy:

often have both count and mass forms.

See how they coordinate well with each other? The expressions between both and and always coordinate with the ending expression, so, often have both a count and a mass forms would be grammatically incorrect.

I think the answer to your question lies under the usage of "a" - which is used as determiner in "have both a mass and a count form". Let me give a similar example first, so we can compare to see why the noun "form" is used as singular:

They have a red and a green apple.
They have red and green apples.
They have a red and green apple.

In first, they have two apples - one of which is green and other is red. In the second, they have apples but we are not sure if some apples have both red and green colors or some of them are green and the others are red. In third, they have an apple and this apple has green and red colors.

So, usage of determiner "a" effects the meaning and form.