The disease shown in "Hell O' Dollies" (later known officially as "The Hell of the Doll Funeral") is identified as Early Onset Doll's Disease. By definition, this means that it happens more commonly later in life — and the early onset version is said to have affected 30% of the world's children. Think about that for a moment.
This is mitigated a little by the official translation- the condition is called "dollification", and while still affecting children only, isn't classified as an early-onset disease.
In "Mold", we're shown that when Mr. Rogi came over to ask to rent the house, Akasaka's dog constantly growled and barked. When Akasaka returned to Japan, he was told that the Rogis had let his dog escape. Given what we know about Mr Rogi's experiments and what was happening to his family, and that the dog was "suspicious" of them ... can we be so sure the dog did just run away?
In "Hanging Blimp", there are stated to be copycat suicides and mass disappearances in the wake of Terumi Fujino's own apparent suicide. Once we learn what happened to Terumi, it seems that the copycat deaths may have been as-yet unknown further of the balloons' arrival.
The twist in "Smashed" is that the honey Ogi had been gifted was not honey at all, but the sap from a giant, sentient tree, that is normally fine with people drinking its sap as long as it 'doesn't see them'. It all begins to make sense when you see the tree as a human, the sap as blood, and the drinkers as mosquitoes. Humans squash mosquitoes when they find them drinking their blood in much the same way the tree obliterates the drinkers. Ogi survived for so long because the godlike tree trusted him, but the other drinkers stole the sap (resulting in Ogi's death) and paid the price.