Thyroid surgery is a very safe surgery.  Complications are rare.

Thyroid Hormone Replacement 

It is always needed following total thyroidectomy as whole thyroid has been removed.  For people who have had hemithyroidectomy, the risk of requiring hormone replacement long term is up to 40% (depending on age and family history of hypothyroidism).  Most common replacement in in form of thyroxine tablet. 

Post-Operative Bleeding 

It is very rare.  This normally happens in the first 24hrs following surgery.  The risk is 1% or less that you may need to go to operating theatre to stop the bleeding and remove blood clot.  If bleeding happens, most/all people postoperatively require admission to Intensive Care Unit (ICU) as they require breathing tube (ETT) for 24-48 hrs.  This is due to swelling of the windpipe (trachea) and surrounding tissues. 

Permanent or Temporary Damage to Recurrent Laryngeal Nerves 

It is also rare.  The risk of permanent damage is up to 0.5% and temporary up to 5%.  Temporary damage should resolve within 6 months of surgery.  The outcome of damaging recurrent laryngeal nerve on one side is hoarse voice and some people develop slight shortness of breath on exercise.  Damage to both recurrent laryngeal nerves is extremely rare and may lead to problem with breathing and require tracheostomy. 

Permanent or Temporary Damage to External Branch of Superior Laryngeal Nerve 

It is also rare.  If damaged it leads to inability to project the voice.  This is most noticeable in public speakers, teachers or people when they are trying to yell.  The risk may be up to 5%, but this damage is difficult to diagnose as there is no good test for it.

Permanent or Temporary Damage to Parathyroid Glands 

Leading to hypocalcaemia (low calcium levels in the blood) is also rare.  Risk of permanent is less then 0.5%  and temporary up to 6%.  For patients who have had hemithyroidectomy the risk is 0%.  The treatment is with calcium and vitamin D replacement.

Infection 

It is extremely rare as well, less then 0.5%.  It extremely rarely requires surgery and is always treated with antibiotics. The best prevention of complications is that your surgeon has had subspecialist training in thyroid surgery.  It has been shown that these surgeons have much lower rates of complications, especially damage to laryngeal nerves and parathyroid glands.