Really interesting thread.
I agree with the consensus that old compost (or even wood chip piles) that hasn't been turned can cause some nasty stuff to be in the middle. If I remember right, another BYCer had trouble with old compost poisoning his flock. I think he had gotten some badly turned wood chips from a tree trimmer or simply had left the trimmings in a pile for a long time before using. (He had it tested, and I forgot what was found in it).
I should add...I use wood chips constantly, from tree trimmers, in my wet Oregon, and have never, ever, had any trouble. It is all exposed to sunshine and rain and constant turning by the birds.
Standing water won't cause botulism, to my knowledge, but it can harbor coccidia in the wet soil.
And I second rat poisoning can be a problem if you used the 2nd generation "first bite" type that can produce substantial poisoning to anything that eats the dead rat. (First generation blood thinner types that have to be consumed over a period of time are much safer for secondary poisoning).
However, a dead rat in itself, though thoroughly disgusting, is often a tasty snack to chickens. I've bagged trapped, dead rats (no poisoning) and forgot to pick them up only to find an empty bag with a chicken running around with the dead rat several days later. The flock was having one of those soccer games for treats. (Ewww).
Chickens are omnivores and opportunists. Fortunately they also have a higher body temperature, about 105 to 107 degrees F, and a higher stomach acid than humans which helps protect them from normal bacteria that would make us really sick.
My question to the OP is...are your chickens exhibiting illness? What makes you think they are "off?"
Have you wormed them recently? What about external parasites?
From the description of your environment, rodents bring in a lot of external pests, and it may be far more likely that you've got a mite/lice problem in the birds causing anemia than botulism in the soil or rat poisoning. (That tends to have very specific symptoms).
My thoughts.
Lofmc