Is methimazole a safe medicine?

Usually. Most people have no problem with Methimazole but, like any medication, there can be side effects. The most serious is a suppression of the bone marrow which will impair the body's ability to fight infections. If a person takes Methimazole and gets fever, infection, sore throat or anything worse than a runny nose, they need to stop the med and call their doctor immediately for a blood test.
Generally yet. There is about a 10% incidence of a skin rash, and some other very uncommon adverse events, but it's generally a safe treatment for hyperthyrodiism.