Side effects may include:

Psychological
Depression or even suicidal ideation, as well as nightmares
Apathy or anhedonia, as well as dysphoria
Anxiety, especially of the social anxiety variant
Decreased alertness, awareness, and wakefulness
Impaired attention, focus, and concentration
Decreased desire, drive, and motivation
Fatigue or lethargy or malaise or lassitude
Sedation or drowsiness or somnolence or sleepiness
Agitation or restlessness
Cognitive and memory impairment
Derealization or depersonalization, as well as mild psychosis
Sexual dysfunction including impaired libido, desire, and drive
Physiological
Dizziness, lightheadedness, or vertigo
Miosis or pupil constriction
Xerostomia or dry mouth
Gastrointestinal disturbances such as diarrhea or constipation
Headache or migraine
Myalgia or muscle aches, arthralgia or joint pain, or paresthesia ("pins and needles")
Restless legs syndrome (RLS)
Parkinsonian symptoms such as muscle tremors, rigidity, hypokinesia, or balance or postural instability
Akathisia, ataxia, dyskinesia as well as even tardive dyskinesia, or dystonia
Bells palsy or facial paralysis
Sexual dysfunction consisting of impaired erectile dysfunction or anorgasmia
Hyperprolactinemia or excess prolactin, gynecomastia/breast enlargement in males, or amenorrhoea or absence of menstrual cycles in females
Bradycardia or decreased heart rate
Hypotension or decreased blood pressure (though this may also be considered a therapeutic benefit)
Orthostatic hypotension (also known as postural hypotension)
Hepatitis, hepatotoxicity, or liver dysfunction or damage
Pancreatitis or inflammation of the pancreas
Warm autoimmune hemolytic anemia or deficiency in red blood cells (RBCs)
Myelotoxicity or bone marrow suppression, potentially leading to thrombocytopenia or blood platelet deficiency or leukopenia or white blood cell (WBC) deficiency
Hypersensitivity such as lupus erythematosus, myocarditis, or pericarditis
Lichenoid reactions such as skin lesions or rashes
Pallor

Rebound/withdrawal
Rebound hypertension via withdrawal on account of tolerance upon the abrupt discontinuation of methyldopa has been reported. Mechanism of action
The mechanism of action of methyldopa is not fully clear.
The Diagnostic and Statistical Manual of Mental Disorders (DSM) defines six subtypes of the disorder characterized as erotomanic (belief that someone is in love with one), grandiose (belief that one is the greatest, strongest, fastest, richest, or most intelligent person ever), jealous (belief that one is being cheated on), persecutory (delusions that the person or someone to whom the person is close is being malevolently treated in some way), somatic (belief that one has a disease or medical condition), and mixed, i.e., having features of more than one subtype.Delusions also occur as symptoms of many other mental disorders, especially the other psychotic disorders. The DSM-IV and psychologists agree that personal beliefs should be evaluated with great respect to cultural and religious differences, since some cultures have widely accepted beliefs that may be considered delusional in other cultures.An earlier, now obsolete, nosological name for delusional disorder was "paranoia". Classification
The International Classification of Diseases classifies delusional disorder as a mental and behavioural disorder. Diagnosis of a specific type of delusional disorder can sometimes be made based on the content of the delusions, to wit,  the Diagnostic and Statistical Manual of Mental Disorders (DSM) enumerates seven types:

Erotomanic type (erotomania): delusion that another person, often a prominent figure, is in love with the individual. The individual may breach the law as they try to obsessively make contact with the desired person. Grandiose type (megalomania): delusion of inflated worth, power, knowledge, identity or believing oneself to be a famous person, claiming the actual person is an impostor or an impersonator.