Succulents can be damaged by soaps. Try either wiping or washing the spots off.

It can be difficult to determine which "soap" is a soap and which is a detergent since the Food And Drug Administration allows detergents to be labeled as soap. Soaps are made by reacting animal or vegetable fats with lye but that too can be difficult to determine but Ivory, Fels Naptha, the Dr. Bronner brands, and most any castile soap would be a good start. Most all dishwashing "soaps" are not soaps, they are detergents.
Most all recipes I see on line suggest mixing a much too strong solution, but many also suggest using detergents which are not effective. One teaspoon of soap per quart of water (3 teaspoons per gallon) is strong enough but even that can do harm to many plants and is a broad spectrum poison that needs to be used with care, although this has no residual affect. Insecticidal soaps are not effective against eggs or larva, however, and must make direct contact with the target insect.
To get the soap ready to mix shave some off into some hot water to make a paste or gel.

Please heed Jean's advice regarding damage to many kinds of succulents, including jade, by the use of soaps. This is true with homemade or commercially manufactured (and usually much safer) insecticidal soaps.

Something that CAN be used, however, is rubbing alcohol. You've probably read about using a cotton swab soaked in alcohol to clean off mealybugs and other pests. You can also use a spray of one part alcohol to three or four parts water. It's very safe for cacti, other succulents, as well as a very wide range of other plants.

But, first of all, you need to find out what these things are! Identification of the problem is important. If you can take some good images, we'll probably be able to ID for you.

I believe the list of true soaps includes Ivory (the bar, not the liquid), Neutrogena (again, the bar), and Murphy's Oil Soap.

FWIW, I got spider mites on my jade a couple years ago and used a commercial insecticidal soap to no apparent ill effect. I'd use that again before a home-made product.

But if you can fix the problem without applying soap, that's the way to go.

This post was edited by DMForcier on Sun, Apr 6, 14 at 16:08

Just make sure you are using real soap. Dawn dish liquid may also be used IMHO but the other dish liquids are too strong.

I've used baby shampoo and cooking oil 1 T of each in a gallon of water on succulents and not had any ill effects. But one thing, don't put them back in the sun until it's dry. keep them in the shade and out of the sun for a few days afterwards.

THANK YOU! You're all very thoughtful to have answered so quickly. While I'm researching soaps, I'm going to try the rubbing alcohol solution.

I didn't know that the soaps wouldn't affect these little specs that multiply at frightening speed and seem to like the tender young leaves the best.