Opossums have a spectacular immune system, and a lower than average body temperature. This means that they don't carry a whole lot of the standard zoonotic diseases that other animals might carry. Although an opossum might get rabies, it's very unlikely. However, opossums do often carry fleas and other parasites, and the potential diseases that go along with those. They also defecate, a lot, and when they get in your attic the droppings can contaminate the area and pose the usual excrement health risks, such as leptospirosis or Salmonella.
Just like humans and other animals, opossums can carry certain diseases. It's possible for opossums to carry leptospirosis, tuberculosis, relapsing fever, tularemia, spotted fever, toxoplasmosis, coccidiosis, trichomoniasis, and Chagas disease.
Although not all opossums (or animals) carry diseases, it is a possibility. This is one of the reasons it is recommended to treat all wild animals respectfully and remember they are not domesticated nor have they received vaccines like household pets.