Diseases are not common. Black Spot (also known as: Leaf Spot) is one of them. It has been named after a fungal infection that causes black spots on the leaves. Black death is another common disease caused by a virus. In that case the flowers often show fine black lines or stripes. For amateur growers there are no pesticides to control these diseases. When the first symptoms show, throw away the affected parts (into the waste bin). This often works well. If the infestation is worse, or gets worse, there is only one solution: lift the plant and dispose of it in the waste bin.
Plagues are more plentiful. The most important plague is: a visit from Aphids. Fighting these is fairly simple. A mixture of diswashing liquid, denatured alcohol and water often solves most of the problems.
Especially in spring, woodlice can damage the flowers and young leaves, but this is never a big problem.
Mice and rabbits as well can pose a real problem. Especially in the winter and early spring, these little animals may label the “budding green” as a welcome addition to their diet. Mice also find seedlings to be extremely delicious.
Snails form no threat to the mature plant, but they do like to devour a pot of seedlings. And all that preferably in but one visit.
With emphasis, I would like to point out here that ants are absolutely no harm to Hellebores. Ants can be annoying because they will carry off seeds of Hellebores, and you may find them emerging in the strangest places in the garden. Is that a problem?