Color cast is entirely an Android problem. If Google would get off its butt and implement color management in Android, you could simply profile the screen and correct the color in software. That is in fact what Apple does with its phones, tablets, and laptops to eliminate color casts - they color calibrate each screen and implement the correction in software. It's got nothing to do with OLED - as long as red, green, and blue are being generated in sufficient quantities, you can have a perfectly color calibrated display assuming the software lets you actually calibrate it. And OLED generates gobs of red, green, and blue - enough to cover AdobeRGB color space and beyond. Most LCDs are limited to sRGB or less (they only use blue LEDs, and a phosphor which converts some of that blue light into yellow, with the yellow substituting for red+green).
Uneven backlighting and dark splotches a LCD problem. You try coming up with an arrangement of lights around a rectangular perimeter which provides even brightness across the entire surface area. LCDs use an complex arrangement of diffusers and light channels to try to spread the light around evenly. It is not precise at all, and very fragile. I had left my laptop closed on a table, and someone signed a piece of paper on top of it. Apparently they pressed down very hard, because the pressure from the pen was concentrated enough to deform the diffusers slightly, and that laptop screen developed a dark splotch right where the person signed.
Pixel noise is due to most LCD panels being 6-bit and using time-dithering (rapidly flickering it between two 6-bit color values) to achieve 8-bit color depth.
Color gradients I've seen on OLED screens, but it's not because of the OLED layer itself. It's something to do with the layers they put on top. It's greatly exaggerated if you look at the screen through polarized glasses. In theory OLEDs should look identical through a polarizer as without. But something they're doing with the layers above it (maybe the capacitive touch layer?) leaves stresses in the material which are obvious through a polarizer.
Burn-in is the one problem OLED does have. But I used my Galaxy S for 5 years without any significant burn-in.