Currently, the UN has the Security Council (SC). This body can veto the majority and unanimous decision of the General Assembly (GA - legislature) without the ability for the GA to override as is possible in the US between the executive and legislative. Likely, it will take another world war before any reform can remove the hegemony of the permanent 5 members (three since the other two vote with the US - US, China, and Russia). Though it will likely not happen, I propose the following:
1) A world constitution, guaranteeing humanistic (no religious domineering as it should be a private matter) free rights (countries could still have their own state churches but stop the killing and mutilations, mm-kay?
2) A multilateral federalism. The US and Canada are bilateral - the balance between the states/provinces versus the national govt. States/provinces are unitary in regards to county/city/town rights. Multilateral federalism would ensure each level of govt would be federalized: city/town, county, state/province/region, nation, supernation/UN.
3) The secretary-general would become a figurehead (more so) and the symbol of the world. He would be the chief justice over the International Supreme Court and have no executive powers, not even reserve powers. The International Supreme Court, however, would exercise pro-active judicial review, meaning before a bill is given final assent, it is judged to be constitutional or unconstitutional. The justices would be selected by weighted sortition to best represent the races, ages, genders, religions, etc of the world.
4) The GA president would be the apolitical and unbiased executive. He/she would hire and fire managers of different departments (security, human rights, environment, etc) on the majority vote of the GA. The GA would be directly elected and could, not veto, but send any bill voted on to a global referendum (similar to Ireland).
5) The GA would be a unicameral (one house) legislature comprised of two classes of representatives: national/ambassadors and proportional/councilors. The councilor class would be divided and voted into 15 councils/committees. These committees are directly elected by proportional representation. Each would only vote on bills relevant to his/her council (security, environment, etc). This would prevent a person from voting for candidate A because he likes his security stance but the candidate is placed on the environment committee instead. Each council would be chaired by a non-voting director of each of the 15 agencies. The ambassador class would, as a whole, approve the bill or reject. A legislative veto, such as 2/3 override by the relevant council's councilors, could be put in place. The bill would then go to GA president (see #4).
A main reason why World War Two was allowed to happen was because the League of Nations, precursor of the United Nations, was incredibly weak and individual nations were free to do whatever they wanted without punishment. The United Nations was founded to ensure another world war would never happen again, and has so far been successful. However, the UN has been unsuccessful in stopping genocides and other brutal conflicts because it lacks the power to do so. With the proper checks and balances in place, the UN could very well unite humanity and usher in a golden age of peace and prosperity, where people pledge allegiance to the species and to the planet rather than nations and borders.
World Police: The reformed UN would also need a World Police force, with powers and authority like a global version of the US FBI. This force should have power that supersedes those of its national, state, provincial, or otherwise lower level counterparts, so when they show up, it's already known well that cooperation is the best course.
World Military - A UN Military should also be created, so that the World Constitution can be backed, defended, and supported if necessary by force. All personnel would take an oath to defend, support, and be loyal to the species and the planet above all else. This way if a certain bully of a nation uses its military to oppress its people or steal another nation's land or resources, the UN Military can just go in and as shut that shit down. To that end, personnel would be sourced by making three service terms mandatory for citizenries of all nations, and should the need to take down a rogue nation arise, personnel from that nation would be barred from participating and if necessary confined for the duration of the conflict to prevent mutiny, insurrection, or problems for operations.
We are moving further and further away from conflict, chances of world conflict between nations are extremely low. The UN should be given more power, especially for the maintainence of "world peace." This is something that we have to recognize, and should all support for the benefit of humanity, world peace.
It is absolutely ridiculous that laws have been made by the United Nations, but the laws are optional. It is absurd that something can be called "International Law" but in reality, is multi-national options. In order for the rules to actually be enforced, the UN should be given more power.