I don't think it's getting better, it is different for sure, though.
It's not only the media coverage that has gone global. The reaction from the West to the events in Ukraine is proof that full-scale global conflict won't kick off as easily as it would have in 70-100 years ago. That's why I don't see the World War III, feared by conspiracy theorists and nationalist hysterics alike. It's just that IF something would kick off on a wider scale, the results would be much worse, touching much more people. The reason why I see it like that, is not so much because of how the weapons used in warfare today have developed compared to WWI and WWII, but rather because of how economically tied and dependant different powers have become.
I think people should find balance between apathy and going nuts. Whenever I follow social media for news about the current events, e.g Ferguson, I feel the urge to facedesk my brains out of my skull. People love to tweet, repost and share everything, mostly not being aware of shit.