Well, nothing was really disproven.
But let's get to the meat of this.
You don't even KNOW how many retractions they have printed in that time, do you? You assume a LOT. You assume so many they are not no longer reliable.
But, you don't actually know how many. And I'm not falling for this. I'm not starting to think "Oh. I guess the NYT is not reliable because they've had so many retractions". This is another strategy Trump does but only weak minded people fall for. Strong minded people will recognize that no actual proof was given; just an insinuating question was asked.
So, instead of asking us, the people who think the NYT is an organization of principle, I would suggest those people who think the NYT is an organization without principle or skill, that you should provide TANGIBLE evidence on which you base your opinion. I would assume that you'd be able to provide quite a treasure trove of answers.
IF you want to prove you are being FAIR in your assessment, then I'm sure this would be a reasonable expectation.
That or posters just prefer to disregards stories that are inconvenient to them baselessly.