The air gap for our dishwasher has been overflowing since we bought the house 20 years ago. It was an annoying problem but not serious. I tried to fix this problem several times. I replaced the hose, I replaced the air gap NO JOY. The air gap discharges into the garbage disposal. The disposal seems to drain freely. Now I think that part of the problem is height distance between the bottom of the air gap and the disposal is about a foot. The hose is about 20 inches long, and there is about12 inches of hose run that is has a minimal slope.
Question does the dishwasher have to discharge to the disposal? I live in Leland in Brunswick county North Carolina, does anyone know the local code? I tried the air gap into a bucket and it flows nicely.

If the diameter of the hose is right and it slips over the connection of the disposal easily then I think you problem is the opening into the disposal itself. Disconnect the rubber hose and shine a light into the disposal and see if there is something in the tube that the hose fits onto that you might be able to either scrape out or rasp out without causing a leak. To me it sounds like a restriction right at that point, especially if the dishwasher will drain out of the hose into a bucket. Good luck.

Letmetellu is bang on with his answer. Your disposal had a metal knockout that might not have gotten totally removed. Check the disposal inlet for a obstuction.

"Question does the dishwasher have to discharge to the disposal?"

No, it doesn't you may remove the tail piece,(the pipe that connects the drain to the trap) and replace it with a branch tailpiece, (see image). But if you change the hose over to a branch tailpiece you will be left with a hiole in the disposal where the hose connected.
In my area we do not use air-gaps. We loop the discharge hose up as high as it will go and strap it up The loop itself is the air gap. It's the plumbers job to install the dishwasher and in al te hundreds of condos and homes thatwe have installed discharge hose loops we have never gotten a complaint about a air gap problem. Regards. Tom

I finally found out why mine was doing this. It was not the diswasher drain, it was the main drain going into the wall from the trap. Too many years of putting cooking grease down the drain had it plugged up. I should have known as once or twice I have had to turn on the disposal the help the sink drain.
Cleaned out the pipe going into the wall, and all is well.

I guess the pressure from the drain pump was forcing the water into the plugged drain, and the pressure build up caused the overflow

Good to know you fix it on your own. Advice: Use lots of water to flush food out of Garbage Disposer after each use. That way you can be assured there is no food left to plug DW outlet. Milo