If the choke is not properly setup and properly used when starting cold you can get many of those symptoms. The car will be very jerky when accelerating, it will lack power, and will sometimes cough out of the carbs (makes a nice sound). Ron's article called Check Your Choke, has nice pictures and instructions which make setting your choke up very easy.

I would check that first. If that doesn't help I would check the timing, the guy who tuned up your car might not have advanced your timing enough. And if this is purely a condition which happens in wet weather I would also inspect the ignition system very carefully for flakey connnections and watertightness.