As posted previously, I have a 1966 Mustang Coupe with a 302 out of a 68 or 69 in it. It has a Holley 4bbl carb, Edelbrock intake manifold, Edelbrock 4v heads, Pertronix Ignitor, custom headers and dual exhausts with Flowmasters. According to the previous owner (who I have no reason to believe is lying to me), the 302 has only been in there for about 10k miles.
When I got the car, it was running painfully rich (most noticeably at idle, though it may be that way across the board, given that it still gets only 10mpg). The obvious sign of which was the great big black spots that the car would leave on the driveway if left idling for any length of time. Also, the idle speed was cranked way up.
When I rectified these things (and a problem with the timing which seems to have ocurred some time after I bought it, though I do not know how), the engine started to run rough. There's a chugging sound in the exhaust which may simply be due to the dual exhaust. (This is the first time I've owned a car with a dual exhaust.) In drive, at a stop, the engine will cause the car to shake with a definite period. In neutral or park, the idle is faster, so the rough running is less noticeable. At higher RPMs, when I am in a tunnel or another situation where I can distinctly hear the sound of the engine in motion, I can still hear an obvious "void" in the engine sound - it sounds like a fast puttering rather than a smooth roar.
I've pulled the plug wires for each cylinder one by one (shocking myself no less than four times

) and I could not detect any cylinder which was not firing. I've yet to complete my tuning of the carbeurator - I still need to finish adjusting the idle jets and I need to check the float levels.
My dad says it's valves - which seems odd to me, given how few miles the engine has on it, but I suppose it is possible, given how utterly sooty the car was running when I got it. He recommended that I finish tuning the carb and take the car for a 4-5 hour road trip to clean up the valves.
Now, my dad's been working on cars since he was in high school, so I usually don't question his wisdom on these subjects. I still want to solicit some more opinions, though. Anyone have any ideas?