A newspaper is not a single entity. In its life it will have hundreds or thousands of employees with a range from good to bad. You can claim that there's a management structure that should know what's going on but they put trust in their employees even if they are ultimately responsible. If a reporter claims a government source said X but doesn't want to be revealed they need to make a decision based on that reporters history. Basically it's difficult to prevent rogue employees from putting out garbage stories.

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Here a more recent article from the NYT examining the original reporting about the Bush scanner story showing how it was mostly misleading and the paper's response to those claims at the time (that they were misleading)

https://www.nytimes.com/2018/12/04/us/politics/fact-check-pr... (See EDIT at bottom for pastebin link)

For any single news organization over a period of time a certain amount of articles will be inaccurate, sometimes purposefully. The NYT has been around for 150+ years and what matters it is how they manage their reporters and sources. We also need to look at the positive accomplishments. Shouldn't that be weighed against the negative when making a judgement of trust?

The NYT is probably responsible for more breaking news and investigations than any other paper in US history. Stories we might not have have known about without the resources they allocated and their contacts (i.e. government or business sources)

I don't think trust is black and white and that people who claim it is may have an ulterior motive. If you dismiss news organizations based on having a few misleading stories without considering what they have accomplished you wouldn't trust any news organization. This of course would greatly benefit corrupt governments, businesses, and people.

EDIT: Here's a pastebin link to the section of the 2018 article where they examine the original reporting

https://pastebin.com/VKHyGARK