Hi there. I'm an environmental scientist, mainly working in the field of air quality, both indoor and outdoor. I'm also a CF patient and a pet owner.
Is the dog a recent addition to the home and is that why you suspect he's had more hospitalizations? It could just be that the current stage of his disease is making him more prone to infection. There were a lot of particularly rough infections going around this winter, even in the non-CF community. I wouldn't necessarily blame the dog, but I would look into a few things, especially if allergies are a problem.
<a target=_blank class=ftalternatingbarlinklarge href="http://www.helium.com/items/114846-asthmatics-often-discouraged-keeping">Pets, Asthma and Allergies</a>
There are a few things to be concerned about, especially if the dog lives in the house. You mentioned feeding and cleanliness are issues. Although I don't have a dog (my husband is allergic) I do have a pet rabbit that lives indoors. Here's how I keep it from being a problem:
1. Water dish gets cleaned DAILY. This prevents bacteria and mold from forming and becoming airborne.
2. His nesting area (where he sleeps) is not in a room where I spent a lot of time. He does most of his grooming in his nest, and that prevents his fur from being tracked all over the house.
3. The rabbit is NOT allowed in areas where I sleep, since I don't want him contributing to allergens that may settle in to my mattress or pillows.
4. I vacuum twice a week to pick up any sheddings or loose hay that got tracked out of his nest.
Pets can be a problem for many CFers, but there are benefits too. With a dog especially, your son is probably going to do more exercise such as walking the dog, than if he didn't have a pet. The downside to having an indoor/outdoor animal is that it could track in allergens, pollen, mold spores, etc.
A HEPA filter (I recommend Bionaire's HEPA tower with independent ionizer) is great for dealing with those indoor issues that may aggravate the airways. There are plenty of CFers who have dogs, cats, rabbits, fish, ferrets, etc. and don't experience any worsening of their condition because of it.