As soon as I entered our room, located on the highest floor of the hotel, I experienced asthma symptoms (I am allergic to pet dander). For obvious reasons, hotels place guests with pets in rooms on the first two floors and usually set aside rooms at the top level for guests without pets.
I asked the front-desk clerk for another room, but he told me that the fourth floor IS reserved for guests who don't have pets and that the only other room available was located on the second floor, which allowed pets.
Thus, it is clear that the hotel has issues with monitoring guests who bring pets when they're not supposed to and with overall cleanliness (a dog in a room for one night would not have caused the breathing issues I experienced).
Orbitz told me that it is up to the hotel to offer a full or partial refund. After being told that I would be contacted by the manager, I tried calling several times to no avail.