When showing colors of medium brightness (between black and white, in this test case the color is gray, or #888888), there are a few darker spots on the monitor. They are much less visible when showing bright colors, or dark colors. Playing with monitor contrast and brightness does not help. It is not a video card issue, since I've been through 3 different video cards, nor a cable issue, since this is behaving the same on DVI and Display Port.
I have also noticed that they are more visible when the screen just turns on, and over a few minutes they become a bit harder to see, but still visible and sometimes annoying.
Here is a photo:
You can see a small but strong dark smudge in the top of the screen, and a weaker, but much larger smudge on the right side. The small one on the top is about 1cm wide and 2-3mm high. The one on the right is about 3mm thick and goes down about 12cm.
What are these smudges, and are there ways to fix them?
An update to the situation
It got worse. Significantly worse. Appallingly worse. Small spots turned to large spots. Eventually the entire monitor was affected. They became big, dim, reddish in color, and had I used the monitor myself, I would've thrown it out long ago, but it was my parents, who were not bothered by it. The monitor lasted for what? 3 years? maybe 2 "usable" years? It's appalling that such a bad piece of hardware could cost 1000$. I had to force my parents to throw it out, by getting them a replacement 27" monitor that I bought for 270$, albeit 1080p (they won't notice), that is SO MUCH BETTER, and lower power consumption, lighter, thinner bezels, brighter, and no spots.
Judging from the amount of traffic this question is getting (I just got notified that it's been viewed 1000 times), I am guessing that a lot of people have the exact same issue. My advice - never buy expensive monitors from Dell. And if you have this behemoth now on your desk, get rid of it, and get yourself a lower powered monitor that's gonna perform much better.