When something big happens in the news, all the other little things slip through unnoticed.
People don't really pay attention to minor news events when there's a big accident/incident of some kind.
ーWhen something big happens in the news, all the other little things slip through unnoticed.
「何か大きな事件が起こると、他の小さなことは全部人の目にも留まらない」
この場合、slip through unnoticed のように言うと良いでしょう。
ーPeople don't really pay attention to minor news events when there's a big accident/incident of some kind.
「大きな事故/事件があると、人々は小さなニュースにあまり注意を払わない」
don't really pay attention to ... を使って言った方が自然な言い方になります。
ご参考まで！
カナダ 
