The Longman Dictionary of Contemporary English lists 'real' as an adverb also, but qualifies it as 'American English spoken'
Even Merriam-Webster's Online Dictionary has the following note for 'real as an adverb:
Most handbooks consider the adverb real to be informal and more suitable to speech than writing. Our evidence shows these observations to be true in the main, but real is becoming more common in writing of an informal, conversational style. It is used as an intensifier only and is not interchangeable with really except in that use.
I, therefore, don't think it's incorrect to say something like "It is a real cool answer" in informal speech and writing!