Common side effects of methadone include anxiety, nervousness, restlessness, insomnia, weakness, drowsiness, dry mouth, nausea, vomiting, diarrhea, constipation, loss of appetite, and decreased sex drive. Weight gain can also be a common side effect of methadone.ethadone is a medication used to relieve severe pain. It's also used to prevent withdrawal symptoms in people who are addicted to opiate drugs such as morphine, hydrocodone, oxycodone, and fentanyl.