When there is a dirty spot on the screen I usually clean the whole screen, that way it evens(cleans) out the whole screen. I make use of 3 sides(corners) on the cloth - 1 side is dry, the next is damp and the third is fully wet. I wipe the screen with all three corners until there are no spots and get a clear screen..
Sometimes you do have to redo some steps to remove some stubborn spots.
But generally one or two wipes and the spot goes off completely.