So far I haven't found a reliable way out. Social media and personal blogs definitely aren't it. In fact, they're feeding the badness.
Interestingly, I feel that paper editions of newspapers and magazines have less broken articles than their websites.
For me, the scary thing isn't that there are biases. It's that pretty much all major media outlets occasionally participate in Culture Wars™. That is, they take an extreme position on some polarizing issue -- whichever appeals to most of their core audience -- and then use every method available to reinforce their "side" and either ignore or try to discredit the "opposition".
But even that isn't the worst of it. The core problem is that both "sides" of such issues are often objectively wrong. Is it even sensible to try extract The Truth™ from two equally full buckets of bullshit?
I feel like this has become much worse recently. Maybe it's just me changing. Then again, there were no Twitter outrage campaigns before Twitter. There were normal outrage campaigns, but they were mostly wars by proxy fought mostly in the media. People observed them and maybe agreed. Right now, almost everyone is an active participant. Which generates news in its own right and skews coverage even more.