An Infection Control Specialist here.
The simple answer is "YES".
This may be more than you want to know, but it's kind of a basic explanation of some bad stuff that can happen. I'll try to keep it on the basic side (trust me, you don't want to know some of the stuff I've been thinking of). It's going to be long (sorry).
Some of the things they are worried about are:
Contaminated water
Flood water is basically a stew of whatever was in/on the area that was flooded.
Things like garbage, trash, sewage (toilet water), decaying items (like plants, food, bodies of humans and animals, building materials) are a concern mostly because of the germs in them that are normally killed/controlled by the ways we handle those items. The flood water becomes contaminated with the germs and may even be a growth media. People walking thru the water can pick up germs thru breaks in their skin (cuts, scrapes, etc.). If the wound is taken care of, they may avoid an infection.
Chemicals like gasoline/oil from cars, truck, and fuel tanks, household cleaners/industrial chemicals mix in the flood water as things either get flooded or damaged by the hurricane winds. Some of these things are just irritants, but some are dangerous (either by contact or by drinking) all by themselves or if mixed with the other substances.
Drinking water is usually filtered and purified before we drink it. The drinking water becomes contaminated by all the same things that are in the flood water. Many illnesses that can cause vomiting, diarrhea, etc can be transmitted by drinking water that is contaminated by them. Some can be spread by even small amounts, like water splashed in the mouth. One big problem is Norwalk (which some people may remember from problems on cruise ships), but there are many other similar illnesses. Since there is no way to handle the sewage, the more sick people you have, the more the water becomes contaminated. They are trying to control this problem by bringing in bottled water. There is also a vaccine for Hepatitis A, one of the big concerns in situations like this.
Contaminated food
Food can be contaminated either just from lack of refrigeration or by being contaminated with flood water/sewage. (works the same way as drinking contaminated water)
Germs can also get onto people's hands from touching things that are contaminated from contact with stool/vomit (like toileting, changing diapers). If you can't wash/sanitize your hands, it's possible to contaminate clean water or food while eating or feeding others.
They are trying to handle this with alcohol handrubs (Purell, etc).
Airborne/Droplet Transmission
Germs like TB, chicken pox, colds, influenza, Pertussis (whooping cough) can be spread thru the air when someone who has the disease in their lungs coughs/sneezes (bring it out of the lungs into the air).
They are concerned about airborne germs because they have large numbers of people together very closely. Because they don't have electricity, the air in the buildings, like the dome, is not being circulated and no "clean" air is coming in from outside to "dilute" the germs.
Some things, like colds, spread quickly and easily, but are not usually serious to people who are in generally good health to begin with. Some things, like TB, don't spread as easily and take longer to show symptoms, but are more serious illnesses. Doing chest X rays would help determine who might have TB and should not be sharing air space with others.
Vectors
This includes things insects like flies, mosquitos, other insects and rodents like mice and rats.
Most vectors mutliply rapidly and are quick to take advantage of conditions. The stagnant water and heat are conditions favorable to mosquitoes, which can pick up diseases like Malaria and West Nile Virus by biting infected people. As the mosquitoes bite other people, they can spread the infection (those infections are not transmitted person to person).
Other diseases can be spread in similar ways by other insects.
Insects can spread some germs on their feet as they walk around. Because they can fly and/or move quickly, they can spread infections from place to place.
Rodents can spread things in several ways; on their feet, by biting, by contact either with their feces/urine or by contaminating food or water.
After the flood
Even after the flood waters are gone, the problems remain.
Receeding flood water leave behind a slime of whatever was in them.
Mold grows on damp vegetation, garbage and things like furniture and building materials.
The vectors will continue to be there until they are killed off or conditions change to make life less hospitable to them.
Water supplies will have to be purified and water systems sanitized before the water that goes thru them is safe (this includes even the supply pipes in individual houses/buildings).
So, the hurricane and the flooding are just the beginning of the problems.
ADDED: i was writing this for a long time, so I didn't see what the poster right before me wrote until after I posted. So, add what he wrote to what I wrrote and you will have a pretty good explanation.