In the history of US paper money, there has only been one case of the wrong color ink being used on an issued note. This was the case of a very, very small amount of series 1990 Federal Reserve notes in which the district seals were printed with green instead of black ink.
The overprints (serial numbers and seals) on earlier notes sometimes will change color due to environmental circumstances. The red ink pigments used in the production of 19th century United States notes (for instance) sometimes will turn a very dark blue color due to oxidation.
More recently, it became popular for certain folks (for whatever reasons), to apply chemicals to alter the color of the red seals on US $2 notes to a bright yellow hue.
The black ink used to display the district seal on your note has been diluted to a lighter color (brown) by whatever spilled on it (probably coffee or coke or the like).