Hi
The highest resolution that a monitor can show is 72 Ppi.
If you monitor is set to say 1920 by 1200 at 72 Ppi and that's the size of your monitor, then increasing the resolution won't change the way it looks, but decreasing it will.
If you are seeing the image quality get worse when you crop it then it must be getting cropped to an area smaller then your monitor and enlarged.
Take an image you are having problems with, and crop it and size it manually to the size of your monitor and see what happens when you apply it.
See if it looks different then it does in the editing program.
It should look exactly the same.
Mike