You don't need chemicals or soap for aphids. I like to use gloves for them, and just gently swipe them off. Once off, they should not climb back on the plant, but others may come. If you don't use chemicals, the good guys are on their way.
Sammy

The 'dust' is probably powdery mildew and is more common and is usually worse in areas where there is high humidity and/or little air movement. It's very difficult to eradicate once it has a hold. You generally try to avoid conducive cultural conditions or treat prophylactically with fungicides. Chamomile tea and neem oil are effective as a preventative against PM.

Try neem oil applications at 2 week intervals for the aphids. Mix a teaspoon of neem and a few drops of Murphy's Oil Soap in a pint of very hot water in a 1 qt spritz bottle. Shake well & add a pint of rubbing (70% isopropyl) alcohol & spritz the plants, making sure to wet the entire plant, especially leaf crotches & undersides. Shake the bottle frequently as you apply.

You want only cold-pressed neem oil because it has the most azadirachtin in it. I use Dyna-Gro's neem oil.

Al

Thank you for the advice. It gets really frustrating seeing new growth immediately attacked and seeing a plant that was doing well get infected by those little creatures. I never thought this little vegetable garden would be so difficult.

The dust I was referring to is the dried out tomato leaves. After a few days of spaying with the soapy water, the leaves dry out and crumble when I touch them.

I will try the neem oil. In the past, I would pinch off cilantro stems because there were so many on them, lined up shoulder to shoulder. I ultimately threw that plant out, along with a bell pepper plant that had too many to pick off. Where are the good guys? How are conditions right for the bad guys but not the good?

There are always more bad guys than good guys. The good guys will come as long as you are careful with what you use to kill the bad guys.

After a few days of spaying with the soapy water, the leaves dry out and crumble when I touch them.

This tells me you are spraying between 9:00-6:00 or your soap fraction is WAY too high. I suspect the former. Spray when you are having coffee in the morning - nothing better than suffocating aphids while waking up.

Dan

I killed leaves with a homemade soap mixture that I found somewhere on the internet. The nursery told me I was most likely overspraying. They said do NOT spray until the leaves are dripping.

I tried rubbing alcohol on one of my plants. Wiping each leaf. That seemed to help.

I'd recommend isolating/destroying any plant with a moderate/bad infestation. Aphids are evil.

Alice

I still say to go to the plant, fluff your finger over the aphids until they fall. If you are squeemish, do it with a glove. After most are off, start your hose, control the spray to the right force, and spray the rest off. If you do this a few times, you will have a number you can handle. Just start watching them carefully, and the ladybirds (lady bugs) will arrive to your rescue.

You will always have to watch for all kinds of bad guys, but what kills the bad guys kills the good ones too.

There are also slugs, snails, and everything else in nature.

Are the aphids killing the plant? If not, the soap will not do much more than water. Once you knock them off, they should not climb back on. In the world of bad bugs, aphids aren't that bad.

Now it is your turn. Someone give me some good advice about thrips!!! cucumber beetles!!!!

Sammy