1. Report the fact that disagreement exists. Phrased differently, stop taking academics at their word when they claim there's a consensus. Do some basic web searches to find people who disagree. Get quotes from them. Stress on the word people; not just other academics but literally anyone disagreeing on scientific grounds eliminates the claim of consensus. Bloggers are fine.
2. READ the papers. Journalists never do this. I cannot express how frequently you can spot scientific fraud by just reading the underlying papers, even as a layman. If you lack expertise maybe you'll miss 90% of the tricks but catching 10% of them is still sufficient to notice something is wrong, and often you don't need any special training. Here are some of my own investigations of bad papers - it's often obvious and most of it doesn't require expertise to spot.
https://blog.plan99.net/did-russian-bots-impact-brexit-ad66f...
https://blog.plan99.net/fake-science-part-ii-bots-that-are-n...
3. Hold sources to account when it's proven that they were misleading you. Report on bad behavior to discourage it next time.
4. Be willing to report stories dug up by other people, even when they make Team University look bad. Note how the reporting Silver refers to hasn't been covered by legacy media outlets even though you don't need to be a scientist to understand what they're saying and how damning it is.
In reality this stuff is easy. Nobody is asking for the NYT to engage in professional peer review of newly published papers. Just not assuming anything a professor says is gospel truth would be a good start, but there seems little chance of that happening :( Journalists depend so heavily on academics for rent-a-quote services and a constant flow of stories that getting tough would be biting the hand that feeds them.