Interesting. Should that really be está à espera? Couldn't you also say (with a change of meaning from "waits" to "is waiting") está a esperar and está esperando?
Oh, I've just seen Paulo's other discussion about this topic here: http://www.duolingo.com/comment/602631. Another accepted translation for this sentence is "The man is waiting for the letter" so perhaps "à" is more appropriate for that version.
So, should I report an error next time I get this sentence? I wouldn't want to learn bad habits? :-)
About está a esperar, almost every source I've looked at has mentioned that this construction is common in Portugal but has died out in Brazil, so I confidently said that in a recent discussion and I was told I was wrong: http://www.duolingo.com/comment/155187
Since we are dealing with medical issues here, should "waiting for the card" (such as medial history card) not be acceptable, since we see the man sitting in a waiting room, waiting for medical attention. He should then rather be waiting for a card (which is shown in the hints as an option) rather than for a letter?
I'm not saying you're wrong to expect that to work (because I'm not a native speaker), but I suspect most things that are called a card in English would be called a "cartão" in Portuguese.
The exception in the hints applies to a card (as in a deck of playing cards) which is indeed a "carta", but we would probably translate that as "The man waits for the playing card" to be quite clear what we mean, nevertheless, plain "card" is a possibility (even though it doesn't have a link with medicine either).