Local problems would be problems you face around you.
The local problems would be less car parking space, women safety, children safety, pick pocketing, drainage problems, shortage of clean water , basic shops are faraway (depends where you live) etc.
National problems would be problems the whole country faces together.
These problems would be national security, fuel prices, jeopardy of wildlife, women security, job shortage, population explosion, poor economy, growing infrastructure, language barriers, culture barriers, food shortage for poor, economy gaps etc.
Hope I helped :)