Nikon's response on the green cast present in the D4/D800 LCD screen is that this is not a defect. According to emails from tech support, the D800/D4 LCD displays are more accurate and set to have a better colors reproduction. The display color temperatures in the older D3s/D700 models were slightly higher which made the images to appear somewhat bluish. In other words, the problem is not with the D4/D800 but rather with the D3s/D700 - the new Nikon cameras have a more precise reproduction of white and colors (as defined by the sRGB color space) visible to the naked eye when compared to earlier models.
There is a separate thread on the NR Forum for D4/D800 issues reported by readers.
Images credit: Benjamin Brolet