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1.
Riddin' dirty is the act of owning/driving a car with expensive and gotty rims. As exemplified below by Jay Z's track "On To The Next One," from his new Blueprint 3 album, Jay Z alludes to "Ride clean, I don't ever take the shoes off."

Jay Z explains how he rides his jeep clean (opposite of dirty), and he never takes the "shoes" rims off; hence riddin' clean(opposite of riddin' dirty).
Bought the car tore the mufuckin roof off

Ride clean, I don't ever take the shoes off

Bought the jeep tore the mufuckin doors off

Foot out that bitch ride that shit like a skateboard

Riddin' dirty
by removerz December 30, 2009
 
2.
Famous song from Charmillionaire. Riddin dirty is someone who is causing and/or making trouble, or someone who is breaking the law.
Man, im riddin dirty.. im carrying more weed then anyother niggers around
by yall dont know what this means April 12, 2006