Risk of redo surgery. Second surgery or redo surgery carries increased risk because your surgeon is going through scarred tissue instead of normal anatomy. Typically the surgeon goes slower and small structures like nerves and parathyroid glands are a bit more difficult to identify. Risk depends on the first surgery. If you had one side/lobe removed and now need the other side removed, redo risk does not apply.
Nerve damage. Damage to the nerves to your voice box and the gland that regulates calcium.
There are several. Someone who has had prior thyroid surgery will have a lot of scarring or fibrosis in the area. This greatly increases the risk of damage to the parathyroid glands that control calcium metabolism, or to nerves that control the vocal cords and speaking voice in a second surgery. Also, if the thyroid extends down into the chest, the surgeon is more like to need to cut bones to enter the chest.