30 years ago she would have won this case easily, but today the courts are so corrupt, and political.
For one thing, Palin has a hard time demonstrating that she suffered any actual damages as a result of this debacle -- which is a prerequisite for the case to proceed. Secondly, the fact that the NYT issued a correction makes it hard to prove any ill intent on their part.
It's always good to get into a position where the defendant in a lawsuit mounts a defense that basically says: "I'm not malicious ... I'm just a moron." But that may be the extent of where this case goes.