The key point here is not whether the noun is countable or not but whether it is countable and concrete or countable and abstract. If the noun is a concrete noun such as girl then it is probably better to say: Is there a girl in the room? or Are there any girls in the room?
Constructions such as:
- Is there any girl in the room?
- Is there any dog on the street?
- Did you borrow any book from the library?
may be considered suspect by some careful grammarians.
However, there are many countable but abstract nouns where any is perfectly acceptable:
- Is there any difference between .. ?
- Is there any way I can .. ?
- Is there any reason why .. ?
- Is there any chance .. ?
- Is there any need to .. ?