Partial answer:
Each rhyme is a:
nursery rhyme
In order:
- Sing a sing of sixpence (Four-and-twenty blackbirds, baked in a pie)
- Humpty Dumpty London Bridge is falling down (credit to CodeNewbie)
- Ring a ring o' roses (sternutation is sneezing - "atishoo, atishoo, we all fall down" - originally about the black death/bubonic plague)
- There was an old woman who lived in a shoe (I can't remember how this one goes, but I'm fairly sure she had a lot of children)
- 3 blind mice (they all ran after the farmer's wife//who cut off their tails with a carving knife)
- Mary, Mary, Quite Contrary (How does your garden grow?)
- Little Jack Horner (sat in a corner, and said "What a good boy am I!") (credit to dennis deems)
Making use of the highlighted sections:
- The regal treat is a pie
- The construction calamity is London Bridge itself
- The sound of sternutation is, onomatopoeically, atishoo
- The unsuitable place is a shoe
- The thing the trio lost was their tails (cut off with a carving knife)
- Mary's flowers (and pretty maids) were arranged all in a row, row, row
- And little Jack Horner's sedentary location was a corner
Putting these all together, and taking their first letters, we find that the threat to Gepetto is
plastic - modern mass production techniques and quick formation of molded figures are certainly a threat to his slow creation of hand-carved puppets