The reason why their hair is two different colors is because in the mindspace, badcop pictures himself with brown hair and goodcop pictures himself with red hair. Their hair is naturally red, so they both agreed to dye the bottom a darker color so bc can feel like he has some control over it too.
The fact that their hair is naturally red/ red at the top is a hint towards the fact that gc is, in some ways, the "original" personality.
However, you may note that their body type is closer to how bc portrays himself in the mindspace. They are taller and more muscular. Besides being this way for practical reasons (they are cops after all, it's good to stay fit), it's to show that bc asserts his dominance when it comes to their physical wellbeing.
Post-movie gcbc/ scribblecop has lots of scars, but they are most prominent on the right side of his face, especially around the eye. This is partially a reference to right-brain vs. left-brain (right=emotion=gc, left=logic=bc). Lord Business focused on the side he associated with goodcop. Of course, the concept of left-brain vs. right-brain has been proven scientifically inaccurate. Similarly, the fact that Lord Business sees goodcop as a separate and opposite "side" to badcop shows he has a fundamental misunderstanding of how the two actually are.
Coincidentally, goodcop is right-handed and badcop is left-handed.
The scarring focused around the eye is also to emphasize that it was goodcop Lord Business was focused on "erasing," not badcop. The scarring is very obvious when gc is in control, you can clearly see his blind eye and the scars through his glasses. When bc is in control, his aviators cover the worst of the scarring, and his blind eye is hidden. Once again, it shows LB's misunderstanding of the cops. He believes he can destroy gc while keeping bc completely intact when in fact, gc's disappearance scars bc on both a physical and mental level. He's just forced to hide it and bury it for the sake of his mission.
Finally, to lighten the mood since this got kinda dark near the end, goodcop is always represented by shades of blue, while badcop is represented by reds and pinks. On their days off, you can often tell who was in charge of their outfit by looking at the color. If they both decide on something to wear, it will most likely be purple or plain black and white. Goodcop likes warm clothes and badcop likes cool clothes.