What seriousness can dental infection cause?

Death. Before the advent of antibiotics, abscessed upper front teeth were one of the leading causes of death. Spreading infections have caused so much swelling that it has closed airways. These are extreme examples, but even smaller infections cause low grade systemic infections. Antibiotics will lessen the severity of the infection.
VERY SERIOUS. Dental infections are nothing to ignore. These infections can and have travelled to the brain and killed people. Yes, people have died from a simple dental infection. If you are experiencing pain, swelling, pus, fever, or other signs and symptoms, you should see your dentist immediately, or go to the emergency room if you are having breathing problems.
Life threatening. Bacteria from dental infections, when left unattended, can result in those bacteria entering the bloodstream where they can lodge in the heart and even travel to the brain resulting in serious medical emergencies that can lead to death. These infections can also result in fulminating infections that result in life-threatening swelling (cellulitis) that can threaten your ability to breathe.
As serious as death. Dental infections can cause bone loss and loss of teeth. They can also affect the vitality of adjacent teeth. They can spread to any place in the body through the circulatory system. Depending upon where they travel, they can affect any organ. Affecting the brain, the heart and the lungs are probably the most serious. They obviously can cause very serious problems and become life threatening.
Abcess. A dental infection can lead to an abcess which is a pocket of infected fluid involving the gum and the mouth. This can track into the gum line or into the jaw. It is noted with pain and swelling. This can be very serious if not treated which includes either a root canal or pulling the tooth and antibiotics.