Clown clothing refers to the mismatched items (by color and type) commonly found on characters in Diablo II. This was caused by adding bright colors to items (caused by various modifiers), and exacerbated by the normal/exceptional/elite armor levels, which made it viable to mix and match very different item types. Leather armor (elite quality) with crowns or other heavy helms, plus metal shields. Or full plate mail body armor with leather caps (!) and other incongruities.
The Diablo III developers are not incorporating specific changes to avoid mismatched kits, but they are working to make armor blend together more smoothly. This can be seen with their gear set design system, and will be enhanced by player color modifications via armor dyes.
A few sample gear sets can be seen below, showing how full armor sets should match up fairly well, while giving the classes very distinctive looks.