Answer: It is hard to tell exactly what the culprits are. It would be useful to know what types of flowers these are--different pests attack different flowers. The ones leaving a "slime trail" are probably leaf miners--they tunnel through the leaves, leaving a silvery streak. The tiny spiders could be mites--but more likely, they are tiny spiders! Aphids are also common pests.
How much have they damaged the plants? If it's just an occasional spot here and there, you may want to just live with the damage. You can expect to see all sorts of insect life in flower beds--and many of the insects may actually be beneficial insects, munching away on the pest insects. Any time you treat an entire planting with a broad spectrum insecticide, you kill off those beneficials too, meaning you lose their help in keeping down pests. (Insecticides can also kill bees--which we all depend on for pollinating our crops.)
I would try using insecticidal soap on the plants where you see pests. Mix it according to the label, and be sure to spray both the upper and lower sides of the leaves. I would spray once, wait a week, and spray again. See if that helps keep things under control. Insecticidal soap is one of the least toxic pesticides, and it should be safe for your cats to sniff around. (I wouldn't let them drink it, though!) Try to spray in the evening, when the bees aren't out.
Good luck; I hope this helps you.
Q&A Library Searching Tips