Check and clear all orifices! Be sure to use a carb cleaner that has Toluene, such as Berrymans. Spray it through all openings, especially the accelerator pump and idle circuit. 

Mine has the circuit clogged for the #2 carb. After trying in vain to clear it, I gave up. I'm told it shouldn't matter ,much.

Check your float levels with the carbs on their back, not the side. And check it in 2 places.

Watch the low speed (idle) circuit screws. There is a small o-ring and washer between the spring and the carb body. When you take the low speed needle out, these may or may not fall out with it. Be sure to replace them.

Replace all the o-rings between the carbs. Remember, these bikes are 20+ years old, and anything rubber is probably hard and dry rotted. Buy them from Tim's. Honda wants you to buy the tubes and the o-rings as one set! You don't want to know the price.

When you replace the screws for the choke plates, use Locktite on them!. You don't need them getting sucked into the intake.

The choke spring must be replaced correctly. When the choke is closed, you should be able to move the plates open somewhat against the spring tension. Let go and they'll snap back. If you can't, take it apart and try again.

When you connect all the carbs together, sync them on the bench. This will give you a nice smooth idle, and save you from doing a synch with the mercury tubes. First, shine a light through the back of the carbs. Turn the master idle set screw so the #4 plate opens slightly, just a bit of light coming through. Then, starting with #4 as the master (it's not adjustable) adjust all the plates so they open just as #4's using the sync screws. I double checked them all with a feeler gauge after the light method.

When you put the carbs onto the engine, after the engine is in the frame, hook the cables up first with the carbs in your lap. Then position the carbs to the manifold rubbers. Grease the rubbers. If they're old, heat them a little. Don't burn them. Work the assembly onto all rubbers. Once you get one side starting on, muscle the other holding the first side so it doesn't pop out. Then push the whole assembly in as far as it will go. The rubbers should be almost up to the carb synch adapter screws. Tighten the clamps securely to prevent air leaks. An air leak will keep you from getting a good idle.

When you are ready to start the engine, do it with the exhaust off! That's right, the exhaust off. These bikes will idle on 4 or 5 carbs almost as well as 6. At idle, you may not feel the difference. With the exhaust off, warm it up, then adjust the idle. A blue flame from all shows that you have the idle circuits clear. If you don't get a flame from one, you know that the idle circuit is not working, and need to remove the carbs and investigate. Rev it up. There should be a nice flame from all. If not, you have a problem. Again, let it idle. Adjust the mixtures so you have an equal flame from each. It's helpful to have a fan on the engine for cooling, since these engines get really hot fast. Trust me, this method is the best for identifying any carburetion problems! Thanks to Ken Watson.

Carb synch at idle: Here's what I found. Get yourself a good set of carb sticks and a carb tuning wrench from an outlet such as Dennis Kirk or Chaparral. Warm the bike to normal operating temperature. Now, you'll have to remove the gas tank, replace the fuel line with a longer version, and set the tank on a stand next to the bike at or about the same height so it will feed fuel to the carbs. Take out the number 4, 5, 6, and 3 synchronization screw caps from their respective carbs. Attach the adapters to the carbs and hook the tubing to the adapters. Place a fan in front of the engine to keep it cool. Start the bike, set the idle to 1000 rpm's and look at the mercury level in each tube. Number 4 is non-adjustable, and is used as the base setting. Now, get the wrench to the adjusting screw and nut for the number 5 carb. Loosen the nut, and turn the screw in or out until the mercury column matches the number 4 baseline. Tighten the nut and move on. The book says that 1.6 inches difference is within spec. but I got them as close as a half inch. Now, do the same with the number 6, then 3, then 2, then 1. It's important to do them in that order. You'll notice the idle smoothing, and the internal racket, clutch noise, etc. disappears! Once they're all about even, you're done. It may take an hour or two, but it's worth it!. It really quieted my bike down at idle, and even though I synched them on the bench as said above, I had one carb that was about 9 inches more than number 4!.