My two cents here :
Much is for non countable and many is for countable , complete agree with paki here.
Now dioxin is the singular and dioxins are plural here, and now if we try to see the sentence here, many is the right one here, because we know that we are counting the different dioxins here which are responsible so now we are left with two choices D&E. Now if we look at option D -> Many of the dioxins that are uncontrolled and North American

hahahahaha (no hard feelings)
So obviously option D is wrong. Now why not E , ok we are talking about the amount of something in a particular non countable substance, here if you dig into it, the non countable is air, so it would be great if we had something like ->
much of the air now days is polluted with many dioxins and sulphides !!
However, like when we ask this question , about dioxins, it would be like How much dioxins goes into the air, because, now here its like we are asking about the quantity of dioxins going into the atmosphere, which might constitutes many dioxins !!
Now paki bhai fruther to add to one of your query about the plural and singular, well it would be really weird to say that plural has many or much , because then i can give you sometihng like,
Much of his hair are gone and he is bald !
In my head there were countable number of white hair, as many as two as far as I could count
Hope this helps
