I don't know if it's "normal" but it's definitely not acceptable. I recently put one on mine (I'll post some pictures later when I have time) and have a number of issues but the color banding is probably the worst and if it's considered normal there's probably no point in buying or requesting a replacement. It's definitely not just visible with the phone off.
What I've found is its visibility is very dependent on the type of lighting. It's not visible with no external lighting and it's either not visible or only barely visible with natural or tungsten lighting. However, under fluorescent lighting (both CFL and traditional office fluorescent tubes) it's very noticeable. Even under mixed lighting it can be very visible if fluorescent is part of the mix. At my office I get a fair bit of natural light from the window but it's mixed with fluorescent light from the ceiling and the banding patterns are visible to the point of distraction. Under CFL lighting at home at night they practically obscure the display.
You, sir, nailed this on the head. I could not have explained it any better. It is really dependent on what light is reflecting off of it. At night or at home with no fluorescent lighting, it is barely visible at all. At the office, I almost can't see the screen. I have not tried this out in the sun. But yeah, it is really unacceptable that a UV coating will cause rainbow banding. It doesn't make sense. I've seen UV coatings on many things, and I don't see bandings on them. I wonder if I can ask for my money back.
Sent from my SGH-I747 using xda app-developers app