Actually its probably not dust. Dust is opaque and therefore blocks light. When projecting black all light should be blocked (obviously it's not and we have what is called video black), therefore dust blocking light would not show up as a color.
More like, a color showing through in black is a problem with the polarizers (maybe LCDs, but less likely). My guess is some minor damage to the polarizer. I can't see it in your image, so its hard to say if it's a manufacturing defect or physical damage (scratched, cleaned improperly) or if it's burns/degradation. If it is starting to burn, that process will continue (abet potentially slowly).