It is important that a world-wide military be limited to enforcing a ban on warfare, and not be used to force nations to change policies. The purpose is to end warfare as a means of solving disputes, not use it to impose policies favored by a majority of nations or a coalition of the most powerful nations.
For example, suppose a branch of the United Nations decided that female genital mutilation should be banned from the world. Suppose some nation is recalcitrant and refuses to accept this ban. The world-wide military should not be used to invade or threaten such a country, to force them to stop genital mutilation. This would defeat the aim of ending warfare. Other forms of pressure, such as sanctions or shaming, should be used for enforcing policy decisions.
Another example might be one country causing pollution that is harming a neighboring country. The offending nation is likely to be breaking international laws. This should be a matter for an international court, not an army. The court will need to have authority to impose punishments, but not military action.
It is extremely important to spell out in specifically what situations a worldwide military is allowed to intervene, and those situations should be limited to stopping warfare or military repression of civil rights and democracy.