This is a very common happening and a rather difficult thing to diagnose for some people...
Your engine had been running fine. Recently it has started running poorly, maybe when its warm, maybe when its cold or sometimes the problem just seems to come and go. The problem shows signs of both a rich and lean running carburetor. You have done the obvious like change jets, replace spark plugs, check plug wires and replace your air filter element, but the problem persists. You and your mechanic are quite frustrated because you can't seem to identify the problem.
Erratic symptoms like these can be the sign of an air leak at the intake manifold or carburetor.
The design of the Harley-Davidson engine and the intake manifold make it prone to air leaks. Improper installation and age are two major contributors to the condition. Symptoms usually develop just after working on or around the carburetor.
Finding an air leak at the manifold is simple. All you need is a can of penetrating oil (like WD-40) with the extended nozzle attached. With the engine idling, direct a heavy spray of the penetrating oil at the manifold gasket area and base of the carburetor. When the spray hits the area leaking, there will be a distinct change in the sound of the engine. If the air leak is major, the change in sound will be quite obvious. Smaller leaks may only create minor changes in the sound.
The engine temperature need to match the times the problem most frequently occurs. If you accidentally spray the exhaust system, you may get a little smoke. The penetrating oil can be cleaned up by washing the bike after the engine cools.
Most carburetors have vacuum lines or fittings attached. The vacuum line(s) normally run to the VOES and on late model bikes, the fuel petcock. If you suspect an air leak, just replace these hoses. You can get vacuum hose at your local auto parts store. Replacement of the hoses is the best way to eliminate vacuum leaks here.
The CV carburetor has one additional area that can create problems. The slide has a neoprene diaphragm at the top. If the diaphragm is installed improperly or develops cracks, an air leak will occur. Problems are most likely to develop just after re-jetting or making modifications to the carburetor. Make sure you properly install this diaphragm after upgrading your CV carburetor. The diaphragm must be properly seated or an air leak will develop.
Using this information, you now have the means to identify the cause of may baffling performance problems on your engine.