Pixel art is a very different medium from what they’re used to, and there are specific techniques that they haven’t learned, largely because they don’t even know such techniques exist. They don’t know how (or when) to antialias or dither by hand. They don’t know what banding is and why to avoid it, nor what selective outlining (“selout”) is and why they need it. They especially don’t know how to correctly choose a good, limited palette. All of these things taken together make for designers at best reinventing tools and techniques, and at worst making icons that suck.
But what can you do? Pixel art isn’t a popular medium, so the wealth of knowledge out there goes to waste. It’s such a pity.
I suggest you check out Pixeljoint—coincidentally it’s down today for a server upgrade, but the community offers excellent feedback for new artists, and the tutorial section has links to some great resources. Pixelation is a great community with many experienced artists from the pixel world and demoscene. You’ll also find a couple of tutorials on an older site of mine, Studio Purloux. One is a general tutorial by my good friend Kevin Chaloux, an outstanding and highly regarded pixel artist; the other is my own introduction to manual antialiasing. That should be enough to get you started.