The only complication I had after surgery involved the anesthesia. The anesthesiologist didn't believe that I get nauseous easily and didn't give me the right cocktail of meds so I was sick the second I woke up and for the next day and a half. Definitely make sure you can speak to the anesthesiologist ahead of time.
What are your levels going in? They like to make sure you're not very hyper ahead of time so you can avoid a thyroid storm. I was slightly hypo going in, had a thyroid dump during surgery (my thyroid was complicated to get out) and then felt fantastic for about 2 weeks.