Alex I have this same exact issue. I've been following other forums and some have reported different screen issues such as a smear effect, blur, red tint, etc. No one has been able to really confirm if my issue was the same one as theirs or if its the terminology I've been using. They thought it was the red pixel issue but I'm not sure. All I know is I have this same exact issue. It's bad when brightness is all the way down, which is a shame because I keep it there to maintain battery.
Now, I don't know if this is my eyes playing tricks, wishful thinking, or anything else... but after the OTA update AT&T released the other day, this problem appeared to be a bit... better in video than previous. I made a video and the complete outside area of what I was looking at was blotchy and pixelated. After the update, there are still some issues but it's more fuzzy instead of pixelated.
there are 3 settings you can play with, to try and workaround this bug (or even fix it if it is a misconfiguration of the device) ...
first, turn off the adapt display setting....it is under Settings>My Device>Display>Screen mode.... you can also play with the options there, and turn on/off adapt display selecting the different options there... THEY DO LOOK A BIT DIFFERENT WHEN ENABLING/DISABLING ADAPT DISPLAY AFTER SELECTING DIFFERENT MODES!!! (this obviously depends on the light circumstances, on certain cases it won't change)
second, turn on/off the "auto adjust screen tone", Settings>My Device>Display>Auto adjust screen tone... it might help a bit with your battery, but i like it better when it's off, because it has WAY MUCH better contrast when it's off
and last but not least, disable the "color adjustment option", it is under Settings>My Device>Accessibility>Color Adjustment....if you have no problems differentiating colors, and it is on, THAT might be your problem... it is designed for people that may have problems looking at different colors, or that can't see colors properly... OR adjust it for you if you have any trouble looking colors properly, i mean, I didn't know i needed glasses until i played with oculist's tools just for fun.....
hope that helps
To take the joke too seriously, my guess is gray-scale mode would be worse for battery performance, since gray light up all three of the sub-pixels (RGB). RED-scale mode would presumbaly be battery-optimal, and that would be a cool effect.
actually, the GREEN led's are the ones that uses the less power, and output the more brightness, and since the S4 has an RGBG screen, where it has more green pixels than any other, it benefits a lot with green images and backgrounds, and a GREEN-scale mode would be the best one for battery-saving/highest-brightness possible...
the worst ones for battery are the BLUE led's.....