Yes, the world is probably a safer place
I think that compared to the cold war era the world is now probably a much safer place. Think about this: as much as the Bush administration for political reasons wants Americans to be scared (easier to control) of terrorist threats, compare the possible danger of terrorist attacks with a cold war-style nuclear war that would probably kill most of us.
Sure, the world is a dangerous place, but I think that the situation is improving even with obvious recent setbacks due to the clumsy policies of the Bush administration.
On a similar topic: have you actually read the text of what Mark Malloch Brown, the British Deputy UN Secretary-General said? Not much at all, and in my opinion definitely not an attack on the American people that John Bolton (US envoy to the UN) has been claiming. Bolton is a neoconservative who has been critical of the UN for years. I also have issues with the UN, but I believe that it is still a good investment - dollars paid for some peaceful results.
I think the question is: why should US policy try to sideline the UN? I think the answer is simple: we are currently the sole military super power in the world and some people believe (misguided, I think) that continued militarism is the best path for long term security and prosperity. I happen to have the exact opposite opinion: security and prosperity will come from strong diplomatic relations with all countries in the world, a smaller and much less expensive military presence in the world, more investments in our own educational and industrial infrastructure, strong policy of energy conservation, and securing our own country.