Some gemstones are expected to have eye-visible inclusions. Emerald is a prime example. If you are searching for a quality emerald that is eye clean, your search could be long and expensive. Yet in that same family (Beryl), aquamarine is commonly flawless.
It is common to find color zoning in sapphire, yet the color of chrome tourmaline tends to be homogenous.
The most undesirable characteristics are those which threaten the integrity of the gem. Cracks, especially those which extend to the surface of a gem, significantly affect the gemstone's durability.
Just remember that inclusions in colored gems that do not affect durability are not nearly as much an issue in determining value as corresponding inclusions in diamonds.