What are the side effects of thyroid replacement?

None if dose right. If your dose is appropriate, there should be no side effects, unless you have an allergy to one of the inactive ingredients ( like the dyes). If your dose is too high, you can get palpitations, tremors, weight loss and other signs of thyroid hormone excess.
Thyroid meds. The most important part of taking thyroid replacement is the selection of chemical form eg thyroid vs thyroxine, taking blood levels, drug interactions and knowledge of the patients liver cyp 450 profile. All the latter factors will decide if you will have elevated elevated heart rate, sweating nervousness, racing thoughts, diarrhea, insomnia....Same symptoms as hyperthyroidism.
Very safe. Unless you over do it, then you can induce what we call "iatrogenic hyperthyroidism." during this state you can feel hyperactive, palpitations, increase bowel movements, tremors, sweating, can't sleep... Long term, this can create problem with heart structure and bone problem (osteoporosis). Some people might get a rash with the pill due to the dye.