According to Living with Chronic Fatigue:

One in ten women suffer from clinical hypothyroidism and up to 40% of those diagnosed with depression also have mild or subclinical hypothyroidism. Frequency increases steadily with age and the elderly are mis-diagnosied with dementia or Alzheimer's when indeed hypothyroidism is the culprit.

Symptoms of hypothyroidism include many of the symptoms of chronic fatigue syndrome leading to misdiagnosis. This is just another disorder that mimics CFS. WTNH.com tells us that, when trying to diagnose CFS, doctors:

......must rule out other chronic fatigue producing conditions, such as hyper-and hypothyroidism, diabetes, fibromyalgia, food allergies, hormonal problems, environmental toxins, sleep disorders, anemia, depression, AIDs, multiple sclerosis, congestive heart failure, systemic inflammatory disease, hepatitis, Lyme disease, lupus and cancer.