Ok, my car has a very, very slight miss at idle. I can hear the solenoid inside clicking, so I know it's working. If I unplug the connector for the solenoid, it instantly smooths out. I figured since this car is new to me, I would just rebuild the carb. I took it all apart and soaked it and cleaned it all out with compressed air. Used a rebuild kit and put everything back like it was. I did verify the float setting, but left all the mixture screws where they were. I also lightened the tension on the secondary air flap some and adjusted the secondary throttle plate to go to full open at full throttle. It was only a little more than halfway before. I was amazed that it fired up this morning. I forgot to prime the carb with fuel, but the thing started up almost right away. I took it for a spin and really like the secondary adjustments I made. No bog or stall and performs smoothly. However at idle, it still has a slight miss. And still when I unhook the solenoid at the carb, it smooths out. Should I just leave it alone and consider it normal or is there something else I can check/adjust?

You unhooked the mixture control solenoid and it ran smoother?

I have an 86 Firebird, it always idled kind of rough (even when completly stock). Sometimes it would smooth out on its own, then get rough again with out me touching anything. Like it was adjusting something. It seemed to run rougher when it was hot. I kind of assumed it was the nature of the beast.

Have you hooked a dwell meter up to it?

No, I don't have a dwell meter yet. This is my first carbed car and am still trying to figure things out. I have learned through this site that I am going to have to get one though.
And yeah, it idles real smooth when I disconnect the solenoid on top of the carb. It is immediate. As soon as I reconnect it, it starts a slight rough idle. Another thing I noticed is with it hooked up and I goose the throttle, it revs up quickly like it should. With the solenoid disconnected, I goose the throttle and its not as peppy. Doesn't bog or anything, just not as peppy.
I'm going out now to put in a new A/C Delco O2 sensor. I don't know what's in it now, but it's very old looking. I have read here that sometimes the aftermarket O2 sensors make the car run on the rich side, so I bought this one from the dealership yesterday.
Will post back after I change it and reset the ECM.

When you disconnected the MC the carb went waaay rich and the computer stopped trying to control the idle mixture and ignition advance. Basically the primary rods are staying in the up position and fuel is dumping into the motor. The result of this was probably a rock-solid idle but no power or ability to transition between throttle settings. When you disconnect the TPS (or go WOT) your MC will go into a different full rich mode and the cycling of the rods into the jets will slow to the lowest setting (around 10 degrees on the meter). They're still dipping into the jets, just not as much.

With everything working properly on a stock motor you may always have a bit of a 'hunt' at idle. Shouldn't really be noticeable though unless you're paying close attention, maybe at a stop light you'll feel the vibration vary a bit.

If you're getting a dwell meter, let us know what it's doing. Your carb settings could be off far enough that the MC can't compensate. It will also give you the peace of mind to know whether everything is working properly.

You may find that the problem is in your ignition, but I'd start with the O2 and meter.