A few spots from incidental leafhopper/beetle feeding and yellowing leaves are normal for common sage, especially for older leaves towards the base of the plant. Sage is a resilient plant and isn't as susceptible to insect-borne plant viruses as more tender garden plants such as nightshades and curcurbits.
I would only be worried if that is happening on newer growth, or if new growth seems to have ceased completely. In that case it could be a nutrient deficiency or other problems with the soil. I would prune back some of the scraggly stems to encourage a bushier, healthier-looking plant. Make sure that you're not over-watering the plant either.
As for your rosemary, that looks to me like damage from a silk-producing caterpillar. The black dots in the silk are its droppings, and the pattern of damage looks consistent with caterpillars. If you pull apart some of the webbing, you may be able to see the caterpillars inside. You should be able to prune off the affected areas to halt the infestation.
What part of the world do you live in? This may be useful in identifying the specific species that is attacking your rosemary.