The main area of reform in the 1800's was the abolition movement. This was the effort to end slavery in the United States. From this sprung many other movements. These individuals were many times very religious therefore many of them also advocated to cure the nations other evils that existed. Religious awakenings developed across the frontier; titled historically as the Second Great Awakening. This consisted of revivals where charismatic ministers would draw on the crowds lust for spirituality and build a large following. These same individuals worked towards the first movement to end alcohol abuse; the first temperance movement. This of course was very much led the female factions of that first and with the effects of alcoholism. an additional movement within all of aforementioned was the start of the women's suffrage movement to attain voting rights. All these reforms existed during the 1800's and eventually they would prove to all be successful if not in the 19th century then in the next century.
I assume that you are talking about the problems that were addressed in the wave of reforms that started in the 1830s and 1840s. This was a time when the US economy and society was changing rapidly. A group made up mostly of middle class people, many of them female, started to try to reform various aspects of society.
Some of the most important problems addressed were:
- Lack of quality education. Reformers like Horace Mann pushed to have more public schools with more qualified teachers.
- Slavery. People like William Lloyd Garrison started pushing for the abolition of slavery.
- Lack of rights for women. The Seneca Falls conference started the women's rights movement in 1848.
There were other reforms during those times, such as ones addressed at improving prison conditions and the conditions in insane asylums. There were anti-alcohol and anti-prostitution crusaders. In short, there were many, many problems that reformers were trying to address.