Does "whereabouts" function as a singular or plural noun?
Solution 1:
Wiktionary marks whereabouts as plurale tantum. Merriam-Webster says that it's a "noun plural but singular or plural in construction". The Collins English Dictionary says that it is "functioning as singular or plural", and the American Heritage Dictionary of the English Language says that it is "used with a singular or plural verb". The Corpus of Contemporary American English has 23 cites for "whereabouts are unknown", but only 3 cites for "whereabouts is unknown". Finally, Google returns 1.1M results for "whereabouts are unknown" vs 191k results for "whereabouts is unknown". So, neither of the forms is unheard of, but "whereabouts are unknown" is preferred by a rather significant margin.
Solution 2:
Since @RegDwight has already provided an answer with strict supporting background information, let me answer this question from a conversational perspective.
I would think of a person's whereabouts as places where he has been. Note my emphasis on places. That's plural. So,
His whereabouts are unknown.
The context here would be that we do not know the places he has been going to.
Solution 3:
The Associated Press 2011 Stylebook records "whereabouts" to take a singular verb.
"His whereabouts is a mystery."
While I believe it to sound and appear incorrect, the AP is the horse's mouth.