You can wipe those off with cotton ball/q-tip damp with rubbing alcohol. Spraying with a squirt bottle can help also if you can't reach the cracks/crevices where the petioles join the stem. Michael, the same works for spider mites. Rubbing alcohol is usually recommended for smooth-leaf (not hairy leaf) plants. I don't know why though.

Lainey, the links for all three photos worked perfectly when I answered - or else I would not have done so. Nor does an answer have to be po-faced to be accurate. Hair at the axils of leaves and flower pedicels, as well as on young flower buds, is a strong indication of L. davidii in the background of an asiatic hybrid. But then, most asiatic hybrids can claim that.

No, it doesn't look like spit (little bubbles), I've seen that on a plant once before. This is a white "fuzz." And I've seen that white bug near it once or twice. I don't think it is spittle bugs, could a whitefly be like what I described or are they like tiny gnats?

Many different types of cacti produce fuzzy white hairs....some much more than others. Looks perfectly normal to me.