Palin is going to have one heck of a time trying to win a defamation suit like this. Since she clearly knows very little about our government/constitution/laws, I'm not surprised that she's unaware of how difficult defamation cases are when someone is as famous as her. Given the Times corrected their writing, this thing likely has no legs at all - just one of those nuisance lawsuits conservatives so often bemoan (yet, in the age of Trump, are all too willing to engage in). 

At least it'll get her what she really wants, though: more exposure. Her clickbait conspiracy website needs more traffic and there's nothing better for that then wailing about how unfair the NYT is. 

http://nymag.com/daily/intelligencer/2017/06/sarah-palin-right-wing-content-farm.html