Unless you have pivot points in the linkage that are too sloppy you should be able to put the selector in park and loosen the adjustment point in the rod and then retighten it.
This can allow the linkage inside the trans to center on the park position.
Of course there are possible reasons other than this (like a worn switch) but it works a lot of the time.
You hit the nail on the head. The first thing to do is a linkage adjustment. I had a Dakota pick up do the same thing. I adjusted the linkage and reset the indicator on the dash and all is well.
