For what it's worth, I've seen this kind of long-term image retention with every Dell desktop monitor in the last 15 years.
My experience is that Dell monitors run hotter than other vendors' displays. LCDs polarize more easily when temperatures are raised, and polarized cells activate with different energy than unpolarized cells. This causes the image retention problem.
You may be able to prevent the effect by running your display with reduced brightness and ensuring you aren't blocking the cooling vents or leaving it enabled in direct sunlight. Once you see the effect, you can clear it by running the monitor at full brightness (for extra heat) and displaying an all-black or all-white screen (either works - consistency is all you're after here) and letting that sit for a couple hours.
Unfortunately, I did see the retention problem with the P2414Q, the model just before the P2415Q. The power consumption specs are the same for both models, and the case design looks similar. I'd be surprised if the thermal characteristics have changed. I can't speak to the 27 inch versions.
Also for what it's worth, I used to get this with my 2009 iMac 27 as well. I'd rip DVDs for hours at a go. The built in optical drive got fairly warm and the CPU ran full tilt doing the encoding. That caused the iMac to retain images. Cinema 30 monitors also had similar problems, likely due to the extra heat from its backlight.
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