There are at least three major ways in which chemical spills and their cleanup can impact society. There are economic impacts, health impacts, and psychological impacts.
I have gone over the economic impacts at length in this question. Therefore, I will not address them again.
Chemical spills can affect the health of people in the area where the spill occurs. Chemicals can leach into the groundwater and can cause diseases. The fumes from spills can overcome people. People who are involved in the cleanup may be particularly susceptible to being harmed in some way as they come into contact with the chemicals.
In addition, there can be serious psychological and quality of life impacts from a spill. People may no longer feel safe in their homes if they are near a plant which has been the source of a spill. The families of the people who become ill will be impacted, of course. Finally, people can experience drops in their quality of life. People who have been accustomed to use an area for recreation my no longer be able to do so if as pill occurs in that area. This can be a real problem for quality of life.
Thus, there are many ways in which chemical spills can impact society.