Petroleum plastics come in many varieties - some are chlorinated and release harmful chemicals into the ground which in turn hurt the surrounding water systems and animals that drink the water. Other plastics that are exposed to sunlight break down over decades becoming only smaller and smaller plastic particles. This is also devastating to humans and animals. Landfills do not exist outside the realm of natural eco-systems and inevitably will effect what is around them.
Petroleum plastics do not break down through bacterial decomposition - it is only through photodegradation ( exposure to UV rays) that their molecular chain breaks apart. This is why plant based alternatives like PLA bio-plastics are more eco-responsible; they break down through bacterial decomposition turning into water and carbon dioxide instead of remaining plastic.