Well, globe thistles are generally pest-free, but these things are listed as non-serious "problems": crown rot, aphids, four-lined plant bug (no problems serious). See the link at the bottom.

See what happens if you treat them with an insecticidal soap that would get rid of aphids or Four-lined Plant Bugs.

Here is a link that might be useful: Echinops

White granulations suggests spider mites?
Miniature droppings suggest a caterpillar or earwigs. One thing about droppings, the culprit is usually near. However, a few larvea look something like droppings to me too. Are they attached to the leaves or loose?

I had something kill a globe thistle plant earlier this year, and damage a number of other plants which are usually quite tough. Based on my readings I think it is four line bug.

I don't belive the four lined bug has killed any of my plants but it disfigures so many of them. I am at war by hand picking and spraying the individual bugs with insecticidal soap. It taks a lot of time and they are very fast. Also I will be cutting down all of the dead stalks this fall to remove their eggs.

I grew globle thistle plants from seed early this year and planted the plugs out in early spring. Had beautiful plants but no blooms. Does anyone know why?

Mine flowered in the second year. Looked great. They only grew half the potential height the first year. I too had an infestation of small black squidgy blobs below the pinicles. This happened in the third year. Not sure which insect caused it, anyone know? The plants looked a bit sorry as a result.

Most likely black aphids. Google and compare the image to what you saw. If not, maybe you can post a picture next season.

If it is a match, all you need are a couple of ladybugs.