World government will eventually come into place one way or the other, but not in a conspiracy laden, clichee form. We already have some world gov. structures and they will rather grow then dissappear.
Severe ecological problems can be dealt with at last (I'm not talking necessarily about global warming, which is of course important, but also about things like fresh water managment, taking care of the oceans and their arising problems etc.)
Limiting human population growth
Let's be honest: we should be very thankful for China's one child policy, as tyrannical and inhumane it is.
While I don't want to see something similar here, we still have to figure out a way to not overcrowd our ecological niche. Which we probably will without a "world president".
"Be fertile, increase in number, and fill the earth" my ass.
I don't think wars will be a thing of the past, at least not for a long time. It won't be one big cozy club from the "start". Depending on how you look at it, that is not necessarily very bad.
Bureaucracy, incompetence and corruption will be rampant at least in some departments.
The whole process of voting, representation and legislation will probably be not very democratic and could possibly frustrate a few billion people leading to ugly things.
As to securely guiding a world economy:
It's a nice thing to believe in Santa or the possibility that bureaucrats will be able to maximize humanity's creative and productive output.
No way this will ever happen. In a sense we already have a world government (and a world bank) and it's clear they're far from super competent. So there will be more free trade, but also millions of silly laws and regulations. Good times for lawyers.