The entire story hinges on the incredible descriptions the speaker gives us and the story that he tells. We can't help but imagine and picture the scene as a movie behind our eyelids as he tells it. As part of the movie, the mariner does mention color quite often, and it brings the narrative to life in certain spots--a little like The Wizard of Oz when Dorothy opens the door and her black and white world is suddenly infused with brilliant color.
The examples of this which spring to mind are the differences in which the mariner notices the sea snakes--go back and take a look at how he looks at them the first time, right after he has killed the albatross, and then how he describes them the second time, when he is able to "bless them unaware" and the albatross falls from his neck. There are grand descriptions the second time with lots of colors mentioned. The use of color on the second description gives the reader the understanding that the mariner is really seeing them and appreciating their beauty as creations whereas the first time he only saw "slimy things". This underlines the mariner's progress as a character and his growth as a person who respects all nature.
In addition, I seem to recall the colors used when he describes Death and Life in Death when they come on the scene. The color here...or maybe even the lack of color...help the reader/listener understand more clearly their purpose.
Lastly, it's worth taking another look at the color and description of the ship's condition when the mariner finally returns home. This description is undeniably important as we also study the hermit's reaction to it.
I'm sure there are other places...go back and skim the poem once again for the use of color in the descriptions and ask yourself how the color helps the reader "see" the picture more clearly.