This is very a reasonable stance, consuming many sources is necessary to understand what sides of an issue may exist. And news organizations may accidentally report incorrect information (hopefully they swiftly retract it when they learn differently).

But shouldn't we not continue to consume sources that have made malicious mistakes? Even if the maliciousness was a bad outside actor feeding incorrect information to ethical reporters, isn't it likely that such a source will make a malicious mistake again? When the consequences are on the scale of directing the country into a fraudulent war, how can we ever trust their reporting on anything of consequence again?

What we're striving for is to consume media sources that produce the least number of mistakes when we're reading them - the number of past mistakes may be an indicator on the likelihood of future mistakes or it may not. I think trying to make any strong statements leaning on historical data should be carefully weighed.

I can't really answer what the best tactic for weighing news sources is since I think that the true measure would need to involve observing the reporters and editors behind each specific article which isn't really feasible. I don't think it's wrong for you to be hesitant about trusting NYT, and feel free to never trust an article written by Miller - I personally think she's shown a lack of care for discovering the truth - but... Eh, balance in all things.