Question

A: Would you like to anything to drink?
B: Diet cola, please.
A: How many would you like?
B: Three paper cups of diet cola.
A: Here you go.
B: Thank you.

(Is the short dialogue grammatical? Would yoiu check the errors in the dialogue?)

Answer 1

If some individual designated what s/he wants to drink, it is typical to give him/her one glass, cup, bottle or can rather than asking him/her how many s/he would want. Once that drink has been almost consumed, the host most likely would offer a refill. "Would you like some more?"

If you are offered something to drink, it is better to ask what is available, rather than possibly requesting something that the host does not have.

Designating "<I>paper</I> cups' might not be correct, if that type of container was not apparently available.

I hope this helps.