This largely depends on your political leaning more than it depends upon fact.
We can actually use the European Union as a sort of realistic example of the advantages and disadvantages of such a system.
Furthermore, I would like to stress. The most important omission from the question is that of the level of autonomy that each of the current countries, groups and factions would have under such a government. As such, I’m assuming that we will have a high level of autonomy. And that we are simply discussing the economics and politics of such a scenario.
If you wished to take this integration to medium autonomy, you could base this off of the structure of Imperial Britain. Or if you wished for there to be low autonomy and a highly centralised government then you could base this off the US federal system.
But, for now, we shall keep it at high autonomy.
Our world is already more connected than it ever has been in all of human history. This would accelerate the trend of interconnectedness and bring about a great increase in wealth across the world, especially for poor countries. Poor countries would have increased access to the wealth of the developed world. While this would bring substantial investment opportunities for the middle and upper classes in the developed world; it would almost completely ruin the working class in these countries.
We have seen this happen before. Especially in Britain, where rising wages and a more competitive developing world destroyed the traditional industry in the rural mining communities in Wales and the North of England.
As a result, expect short, but more likely, medium-term political instability coupled with a rise of anti-globalist sentiment.
Once again, this can be seen in a lesser form today. Where after the crisis of 2008, many working people were hit hard and the middle class was severely damaged. The consequence of this is that the richest in society managed to get richer, while the poor saw their opportunities shrink. Many people would get annoyed at migrants coming and working in their own countries.
Matters of immigration are by nature, highly controversial. While many argue that immigration is better for society in terms of economics, and indeed this is true, the main concern comes at the cultural level.
Higher than sustainable levels of migration from vastly different cultures often cause fragmentation within the broader society. Different cultures who do not necessarily get along will be forced into close communities within cities. This is happening today. And will likely far exceed assimilation level causing cultural pockets to express themselves in different levels of society.
This will likely be the largest issue facing a global government.
The issue being, that people want to live with those they seem as being from the same tribe.
For a global government to succeed, there would have to be a body that regulates the cultural makeup of different regions of the polity lest civil movements tear the union up from the inside.
This is a tricky one.
Essentially, I personally would regard a global currency as a disaster.
It would in effect, be a form of global feudalism.
It would prevent poor countries from devaluing their currency to attract investment, keeping them poor.
I’m not exactly sure on the utility of this, as this has been suggested for the European Union – but it is possible to have a global currency with different levels.
I.e. a global currency for rich countries, one for middle-income countries etc.
Regardless, the question then turns to trade routes and human capital.
Do we keep things the same? Where would the centres of administration be?
London, New York City, and others are good contenders. But then surely a country like China would feel left out.
This is the tricky part. When economics meets politics.
This is entirely hypothetical.
And then, while the world does look like it is going towards a more globalised and integrated society, how does this come about?
A fairly loose union of all of the countries is possible. But anything similar to the global governments from sci-fi books and movies is impossible to bring about without the use of force.