What problems can come from a chlorine bleach overdose?

Death... Overdose implies deliberate intent...Seek help and don't do it! Irreparable life-altering esophageal damage may occur if you survive -and that can be miserable indeed.
Usually nothing. Comercial chlorine bleach does not taste very good and an overdose (high volume) takes a conscious effort consistent with intent of self harm and emergancy medical care is needed...911. However amounts inadvertantly swallowed during splash or from hands to mouth will not require any medical care at all.
Bleach poisoning. Sodium hypochlorite is found in bleach. Poisoning sx's may include: "burning, red eyes, chest pain, coma, coughing (from the fumes), delirium, gagging sensation, low blood pressure, pain in the mouth or throat, possible burns on the esophagus, skin irritation of exposed area, burns, or blistering shock, slow heartbeat, stomach or abdominal pain, vomiting" REF: