https://www.telegraph.co.uk/business/2025/01/07/five-times-f...
https://www.bmj.com/content/376/bmj.o95
https://reason.com/2021/12/29/facebook-masks-false-informati...
Even when they aren't wrong, they can be biased. See for example:
https://www.allsides.com/blog/media-bias-alert-politifact-fa...
Also, compare and contrast how they handled Sanders and Trump's presentations of substantially the same claim:
https://www.politifact.com/factchecks/2015/jul/13/bernie-san...
https://www.politifact.com/factchecks/2016/jun/20/donald-tru...
There's an entire site dedicated to pointing out more examples, aptly named https://www.politifactbias.com/ . They show their work in great detail.
It's trivial to introduce bias by simply being selective about who you hold to greater scrutiny (https://slatestarcodex.com/2014/08/14/beware-isolated-demand...).