1. Nigeria is a colonial creation.
This country was created for British colonial adminstration. It is a known fact that not until some 9 years before Independence were the locals and indigenes allowed a say in the decision making of the country. Nothing has been done to indigenize our rulership of Nigeria better than the colonialist had done. We continue to run a system purposely created and rigged to exploit our lands to benefit a foreign empire.
2. Nigeria's military heritage
The question of whether the military inclusion is legal is a question that needs to be discussed. Was there any provision in the 1963 Federal Constitution that makes it possible for the Constitution to be suspended? Among many other questions we need to discuss. The autocracy of the military led to a civil war, created a loopsided civil service, implemented economic damaging policies and ballooned unnecessary expenses in running government. I'd also dare to add that this heritage made criminals to be treated as statesmen.
3. A Wrong System of Government
I think the presidential system is one big evil the military left us with that's greater than any wrong the colonialists may have done. It puts enormous power in the hands of appointees (Federal ministers and MDA heads) and make elected representatives (Senators and MHRs) look like public opinion specialists at the best. The parliament is not a house of policies but one of oversight over the appointed policy makers. It duplicates responsibilities and increases overhead cost unnecessarily. The military seemingly love the presidential system because it makes it easy for them to be participants and manipulators. The parliamentary system is better suited for Nigeria. The country made more ṣtrides in the tumultuous first six years old Independence than the remaining 54 years added up together.
4. Treating Business as politics.
Things like railways, airports, mining, natural resources management and agriculture are business that should be managed by business people for the country's profit but it is being managed by politicians for a few people's betterment. Even prisons in some nations are privately owned. One has to wonder while government in Nigeria goes borrowing to fix rail travel when privatization (not transfer to friends and family) maybe through an IPO would have created a better business atmosphere over this critical sector.

These are a few problems with our Nigeria today.

The structure of government and the lack of a national identity.