A global government could never be established unless there already existed a rather homogenous global community to begin with. In other words, war and competition would no longer exist while culture and language would be mostly the same. Globalization is also a bad idea because it would ultimately destroy liberty and freedom. By it's very nature, it would have to be totalitarian. It has been shown that, historically, more, smaller nations produce more overall liberty while fewer and larger nations lessen liberty. A single global government would be the ultimate dictatorship, no matter how well-intentioned it might be.
A global government would fail to give radically different cultures the ability to flourish. By creating a global government, the external fighting between nations and cultures would have to be quashed, which is too formidable a task for humans who place a high value of individualism and self-indentification can accomplish.
A global government would not be possible and would be a horrible idea. It was an idea the Hitler had and other dictators would love the idea if they could be in control of the world. But it would be horrible for freedom loving people that wanted to live their own lives.
It would be very hard to keep track of all the different bodies it would take to run a global government. The government officials could get away with all kinds of things. Not to mention, how hard it would be to get the people of the world to come together and agree on what leaders they would want to run the world.
One of the main ways for a government to be effective is for it to be located nearby it's population. Rome had difficulty because as it was overstretched it was not able to keep tabs on distant territory. Further, the earth has so many people that consensus making would be too hard.
I do not think that something like a global government to be a plausible. While some people may think that such a thing would promote peace, I think that governments around the world would not be able to work together where such an idea would work. I think a global government would only work if all the countries in it were allies.