A newer/better calibrator will do a better job. The Spyder 3 is very old now, the technology has improved significantly.
Which Spyder3 is it? Express, Pro, or Elite?
The fix I gave for one photo won't necessarily work on another photo. You need to show me your photo.
Not the whole photo, of course. I need a 100% crop from the problem area.
So sorry about my delayed reply. Glad you like it. Download the PSD here.
Even though the Clone layer is first in the stack (and you can certainly add the blank layer first if you wish) the cloning is the last thing to do. Do the CM and Levels layers first, then come back to the Clone layer to gently (low opacity brush) reduce the worst remaining stuff.
I don't think there can be any doubt that the screen on a $299 laptop will be pretty ordinary.
But there's equally little doubt that a new calibrator which is made for Windows 10 and LED screens will do a better job than one which was manufactured before Win10 or LED.