I did not create the following variables, the state I worked for did...They have one variable coded W if you are white 0 otherwise. A second variable is coded 1 if someone is African American 0 otherwise. Some individuals are not in either group, there are not very many probably although the exact number is not certain.

I am not sure how to interpret the slopes in linear regression for these variables. I assume that you would consider the slope for say Whites as the mean difference between Whites and the "other" category which is neither white nor black, even though no variable actually exists for other. They would simply not be coded into white or black.

Because of mistakes and the fact that customers can self select a small number of customers are in more than one category (for example they are listed as white and black, or white or other). I know this violates the dummy variable rule. How serious is this if the number is very small (it might be a 100 of 40,000 cases)?