In our City, this is considered a freedom of speech issue. If they are on a public sidewalk they aren't required to have a permit so long as they leave 4' of clear space on the sidewalk, but if their cart were to cause someone to trip, it would be a civil matter solely between the injured individual and the JW as to how to deal with the legalities. If you were standing on the sidewalk and someone tripped over your foot as they walked past, they could sue you and they could name the City in the lawsuit, but they wouldn't likely win unless some blatant negligence on the part of those named, could be proven.
When JW's put their carts on private property such as at a shopping center, they'd have to get permission to do so and the shopping center official becomes responsible for any injury that might occur as a result of allowing this activity to take place. This would likely be covered by the shopping center's Liability Insurance
In the case of the JW's carts on public sidewalks, if there were to be some accident, I'm guessing the Watchtower would throw the publisher under the bus and say that use of the literature cart is part of the individuals personal ministry and is done of their own volition. I'm guessing they'd say that the individual JW is therefore responsible for any outcome.