what factors could influence the suppy and demand of a correctional officer's position.
Location of the prison/jail -- whether it's near a high crime area.
The state's, county's, city's funds for jails -- whether they are releasing prisoners because of lack of funds.
The political climate of "law and order" vs. a more lenient approach to law breakers.
how a correctional officer's pay is determined and how the salary is structured.
This varies between the federal government and the individual states, counties, and cities. This site has information about federal corrections officers.
http://www.bls.gov/oco/ocos156.htm
To get information about your local corrections officers, you could check Google for your state, city, and county.
In addition to the previous answer you should consider that this is an economics question. As such the price of labor (funny way to say salary, but this is what economist use) is determined by supply and demand.
The price (wages) of labor is determined by the demand for correctional officers and the supply (qualified applicants who are actively seeking employment. The limiting factor is that in the US in most, if not all, situations we do not have perfect competition. In the case of correction officers we have such items as the costs of overtime, union contracts and political pressures.
I hope that this answer has been helpful.