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I have replaced my MacBook retina Display with a brand new one, but then the screen flickers with colors and when I move the mouse pad it stops and even if I put it on safe mode the display works very fine. What could be the problem and how can I solve it.

It appears as if you didn’t connect the display wire properly to ur motherboard. If that is not the case u could try making a time machine back up and reinstalling OS X from recovery