Let us begin with some background information ( A - C). 

A. Prior to the advent of plastics and disposable cans, waste was typically organic, and after drying or biodegrading could be used effectively as compost, a key ingredient in organic farming.

B. After the waste dries, worms and fungi further break up the material. Aerobic bacteria manage the chemical process by converting the compost into heat, carbon dioxide and ammonium. The ammonium is further converted by bacteria into plant-nourishing nitrites through the process of nitrification.

Traditionally, the composter piled organic materials until the next planting season, at which time the materials would have decayed enough to be ready for use in the soil, whereby requiring little working time or effort from the composter and it fits in naturally with agricultural practices in temperate climates.

There are numerous ways to create compost though. For our purposes, we will highlight the "heating process, block system" which is effective in creating large quantities of compost; a practice prevalent in Talmudic times.

"The heating process is based on a continuous block system. That is, new blocks are being made all the time and piled up. On the first day, a block is made by building up layers of materials collected for composting. After two days, when the block has started to decompose, the air is forced out of the block by trampling over it. On days two and three, new blocks are built next to the first block. On day four, a new block should be built on top of the original block, cutting it off from the outside air totally etc." Farmers commonly piled the compost blocks in public property which allowed for ample trampling. [Bava Metzia 118, Rambam Nizkei Mammon 13: 15, Composting in the Tropics II, Wikipedia].

C. Plumbing was extremely rare until the development of modern cities in the 19th centuries. At about the same time, public health authorities began pressing for better waste disposal systems to be installed. Earlier, waste disposal systems merely consisted of collecting waste and dumping it on ground or into a riverfor minimum production quantity).

Up Up and Away: Kiddy Litter or Kitty Litter invokes the following five laws:

 1. One may not discard his/her broken wares in public property. Doing so, he/she has illegally created a stumbling block and is liable for physical damages incurred by a stumbler (or his/her livestock)  [Choshen Mishpat 410: 20, 21, 417].

 2. If one's wrecked wares land in public property inadvertently, he/she must pick it up - irrespective of whether he/she wants to retain ownership on the shards. After ample time to pick it up has passed, the shards become a stumbling block. Beit Din can hold the owner liable for physical damages incurred by a stumbler (or his/her livestock) as long as the owner retains ownership thereof. Were the owner to relinquish ownership thereof; no one owns the stumbling block or intentionally placed it illegally in public property. Beit Din cannot hold the original owner liable. The Heavenly Court will prosecute the issue [Choshen Mishpat 410: 20, 21, 412:2].

 3. Was one permitted to pile his/her organic waste outside his/her home in public property? It depended. During the season, typically a month or so before the planting season, it was permissible to so and even allow for the public to trample on the compost. Other times during the year, it was forbidden to store waste in the street. Nevertheless, during the "off season", one is permitted to remove the refuse from his home to the street temporarily, with the intention to transfer it to a landfill immediately [Bava Metzia 118, Rambam Nizkei Mammon 13: 15, Choshen Mishpat 414:2].

 4. When permitted to place waste in public property, is the owner liable for damages incurred by a stumbler?  The right to place his/her compost in public property does not absolve the owner from liabilities for damages. As with general stumbling blocks, Beit Din may collect for damages incurred to the stumbling person or livestock, yet, in a special dispensation, the Torah does not vest Beit Din the authority to collect payment for damages incurred by another's inanimate property resulting from the obstacle. A Halachic authority should be consulted with regards to one's moral obligation nevertheless [Choshen Mishpat 410: 21 see also Ketzos HaChoshen].

 5. May one store compost in the street of a modern city with a built-in plumbing infrastructure? No. In modern city's it is generally always "off season". (One must follow the accepted local custom) [Aruch Hashulchan 414].

Application:

Unless there is no room in the dumpster ( as often happens during garbage strikes) it is unacceptable to leave trash in the street. The Berger Boys predicament allowed them to do so "temporarily" though until they can dispose of their ammo properly. Similarly, one may leave the bags on the side, if the garbage collectors will pick it up immediately (provided this complies with local law). Were one to inadvertently hurt themselves on the bags, the boys would be liable if they were not minors (younger than thirteen years old).

If Grandma is able to do so, she must not leave her broken wares in public property. [It is probable though, that Grandma would not be in a physical position to chase after the umbrella].

Grandma Bertha did not intentionally create a stumbling block. Additionally, she relinquished ownership of the shards. Beit Din therefore has no premise to hold her liable for physical damages incurred by a stumbler. Nevertheless, as she indirectly caused damage to someone else (if she was able to pick it up), she has an account to clear with Heaven.