No terrorism, no wars, no conflicts. Countries start working together more closely to solve problems, all countries use their military budgets on other things. Police exists though. There can still be bad people and criminals, but no corrupt or asshole politicians exists anymore. All people who works in government are good people and very intelligent.
No. If world peace began today it would be broken before my pets died anyway.
There won't ever be another person working in government who will bad. No bad people can or will try to get into politics. Imagine how much better healthcare would be everywhere and how much more resources would go into curing diseases.