There were two main problems that were caused by Prohibition. These were a breakdown in the respect for the law and the growth in the power of organized crime.
After Prohibition was imposed, many people felt that there was no reason for them to obey the law. They felt that drinking was an okay thing to do. In fact, they came to feel that going to speakeasies was a fun and glamorous thing to do. Everyone knew that alcohol was widely available. This led to a decrease in respect for the law, which is a bad thing in any democratic society.
At the same time, there was a much more tangible negative impact. This was the rise of organized crime. With so many Americans wanting to drink, only criminals could satisfy the demand. The demand was so huge that the organized crime syndicates made huge amounts of money. This helped lead to the continuing problem of the presence of organized crime in the United States.
These were the main two problems that were caused by the attempt to ban alcohol.