Tiny white bugs on Japanese Holly
Hi, Well it's hard to know what those white bugs are without seeing them or having a better description. Do they crawl on the plant or do they fly off when you go near them? Give us more to go on with your bug description and see if you can tell what they are doing. They could be white flies, but they could be something else.
As far as the black spots go, that's probably a fungal situation due to moist conditions and has nothing to do with your insect pests. Again, without seeing how damaging those spots are, I can't say exactly what's going on, but if the plant is covered in them, you may want to try a fungicide on the shrubs. But, if they aren't widespread, I would not worry about them.