A study of the medical literature indicates that mental symptoms are a common symptom in Graves' disease. According to the authors of the study,
"Antithyroid drugs combined with beta-adrenoreceptor antagonists are the treatment of choice for hyperthyroidism, as well as for the psychiatric disorders and mental symptoms caused by hyperthyroidisim. A substantial proportion of patients have an altered mental state even after successful treatment of hyperthyroidism, suggesting that mechanisms other than hyperthyroidism, including the Graves' autoimmune process per se and ophthalmopathy, may also be involved. When psychiatric disorders remain after the restoration of euthyroidism and after treatment with beta-adrenoreceptor antagonists, specific treatment for the psychiatric symptoms, especially psychotropic drugs, may be needed." Unfortunately, the question of whether these patients might be hypothyroid rather than hyperthyroid isn't addressed and the only parameter reviewed is the TSH.
Early on, the physician Robert Graves described Graves' disease as being associated with symptoms of exhaustion psychoses and delirium. With patients being diagnosed earlier and the effectiveness of anti-thyroid drugs, these symptoms are no longer common. Other mental symptoms, such as moodiness and irritability, are, and they too respond well to corrected thyroid hormone levels.
Although this study is fairly recent (2006) it doesn't address the fact that euthyroidism is (although technically it shouldn't be) based on the TSH level and the fact that after remission or agressive treatment, hypothyroidism is common. Mental symptoms, particularly depression and bipolar and unipolar episodes, are commonly seen in untreated and under-treated hypothyroidism. A low TSH, according to this study, is likely to be associated with mental symptoms, but there is no correlation with thyroid hormone levels or the fact that the patient may be hypothyroid and still have a low TSH. This seems to another connection or possible reason for persistent symptoms in patients deemed "euthyroid."
Buevicius, Robertas and Arthur Prange, "Psychiatric Manifestations of Graves' Hyperthyroidism," Central Nervous System Drugs, 2006: 20(11): 897-909.