Can PET bottles that are left in a hot car or put in the microwave release dioxins?

No. PET does not contain dioxins, nor can it produce dioxins, and no dioxins are created in the manufacturing of PET.  Dioxins can't be created without the presence of chlorine, and PET does not contain chlorine.  Dioxins are a group of compounds sometimes formed by high-temperature combustion (over 400°C) and certain types of industrial processes involving chlorine.  Consequently, dioxins can't be produced when a PET container is heated or microwaved or frozen (all common urban myths).