Precaution should always be taken when using any household cleaning product. In the event that bleach gets on the skin, in the eyes, is inhaled or ingested, exposure may have minor, temporary effects, but harm is unlikely if promptly followed by first aid treatment as noted on the product packaging:
According to the 2007 Annual Report of the American Association of Poison Control Centers' National Poison Data System, the number of incidents reported to the centers about bleach (sodium hypochlorite) is indeed higher than for other cleaners (bleach is in more households than any other cleaner), but the percentage of serious incidents is much lower than many other household cleaning products. In fact, the serious incident profile for bleach places it on a level between shampoo and dishwasher liquid.
No studies have connected household use of sodium hypochlorite bleach to dioxins.