I never used these modes because "zoom map" and "rear view" buttons from "Control" section completely satisfy my needs on navigation.
But it's very interesting to hear the examples of "3D Mode" and "Slide Mode" applications from other players especially veteran ones.
Please, feel free to tell your stories where these modes helped you somehow
Slide mode allows you to move across sector boundaries by sliding the view which is useful when a planet is at the edge of a sector so you can position your exit from a jump at a decent magnification for example.
3D view is just that ... a 3D version of the map that you can rotate in all three dimensions to get a feel for the relative positions of things.
At least that's how I use them. I'm sure other pilots will have other uses