What problems could arise when too many people living in a small area?

Depending on the time frame and circumstances... a big one would be limited resources. People need to eat and need a lot of space to grow and maintain their own resources or be able to import all they need with a very healthy economy. Also any kind of health issues or epidemics would spread much quicker in a small area with a dense population. Those are just a couple off the top of my head.