I'm so glad your puppy is doing better. I know all too well about neighbors throwing food in the yard. My landlord sometimes throws chicken bones - COOKED - in the backyard and my dog has gotten more than her fair share of stomache ailments from it.
Once I had taken her to the park and she found something some moron decided to throw on the ground and not in the trash and that night started a month long chicken and rice dinner w/ a lovely side of constant diarrhea and at least 3 trips to the vet with x-rays. And medication. The first x-ray they couldn't even see much cause her belly was so disdended! By the end of the month they took another one and the compared the 2 and the doctor took it to another vet for a 2nd opinion and he said, "Is that the same dog?"!!!
Now I'm quite the paranoid "mother" and she doesn't get to sniff too long anymore!! My goodness, she'll eat anything. Goodball!
I agree, tell the neighbors to stop the food tossing crap and if they don't, send some poops over to their side!! Fair is fair!!