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?)

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 "paper cups' might not be correct, if that type of container was not apparently available.

I hope this helps.

The short dialogue you provided is mostly grammatically correct. However, there are a few errors that can be corrected:

A: Would you like 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.

In this corrected version, there are a few changes made:

1. Instead of using "like" in the phrase "like to anything," it should be "like anything." So, "Would you like to anything to drink?" should be "Would you like anything to drink?"

2. The phrase "Three paper cups of diet cola" is correct, but it's more natural to say "Three paper cups of diet cola, please." This adds politeness to the request.

Apart from these minor corrections, the dialogue is grammatically accurate.