First and foremost, the most common post-operative complications are pain, swelling and bruising. It is not always that an extraction results in one of these risks, but sometimes even a slight inconvenience can lead to exceptional cases suffering from damaged nerves, adjacent teeth/fillings, sinus, or a jaw fracture, alongside a likelihood of leaving a root in place.
Mostly, following the post-operation guidelines imminently can help you manage any possible outcomes.