This has given me a good idea for a new thread: Designing One World Governments For Fun And Profit!.
Because I would be running it. 
It seems with recent events in Libya, Egypt, Iraq that some countries are hardly ready for a country government, let alone a world government.
If so, and you mean a strong world government, I think global civil war is also inevitable.
Now, as for weak world government, we already have it in the form of the UN.
I like weak world government.
One way to keep it weak is to have competing centers of world and near-world government.
A good example of this is the British Commonwealth. The US should apologize for eighteenth century unpleasantness, and then join it. I like Barack Obama, but Queen Elizabeth II cannot be beaten as a benign leader of billions.
No that isn’t a good example. She isn’t a leader of anything. She is a classy figurehead but nothing more. She has no real power. The suggestion is asinine in a U.S. perspective even though the UK is one of our most valued allies these days but what would being a member of the Commonwealth actually do for the U.S.? We could be like Canada and Australia and get pictures of a classy old lady on our money and someone to pose at grand events but nothing more. That isn’t a world government. It is the political equivalent of Vogue magazine. In any case, the Anglosphere is very important (and the U.S. is already a de facto part of it) but it isn’t the whole world by any stretch.
I’m not a tremendous fan of power. As previously implied, I think a truly powerful world government would create great resentments and probably cause more wars than it prevented.
As for a specific reason why one-world government would be bad, this planet is not an optimum currency zone. So, at least economically, an optimum world government should have less real power than the Eurozone.
The OP is asking what are the drawbacks of a world government, so I’m presupposing the existence of such an organization.
A bunch of treaties that not every country has signed up to, that don’t have clear penalties and require members to vote (and the big guys can incentivize the little guys to vote the “right” way), is the situation now.
If we’re saying things still play out like that under OWG, and the big boys of a region can still have dominion over a region, then how does OWG even differ from the many multilateral agreements that we have in place now?
This is not the same as a world government.There is some economic competition between US States(though not as much as there could be). You are assuming a one world government allows any competition between states. It may allow some competition or it may not. That is the very big risk you are taking on the economic decision or policies of a world government.