Can a single transaction have multiple outputs going to the same address?
It is possible. Here is an example: http://blockchain.info/tx/4199f709bfab79f54938e80e11dc75c21a95e3183f8e8994306f5ff272fde42a

However, the bitcoin-qt GUI doesn't allow creating such transactions.

Such transactions might be useful in the context of colored coins, or where encoding information is involved.