These look like adventitious roots, which can develop on various vegetables, herbs, and even some shrubs. Adventitious roots (or the beginnings of root growth) are those that occur on parts of the plant that normally don't have roots, like above-ground stems. The triggers for such growth can vary and aren't completely understood, but on edible plants they usually aren't a cause for concern. If individual stems have a particularly high number of these growths, you can trim them off if they're bothersome.

Yellowing of the foliage on certain stems may indicate root stress or a disease has infected part of the branches, in which case you can trim that portion off as well. If the root nubs seem more associated with yellowing stems, then perhaps a pathogen that isn't very virulent is responsible. Fortunately, rosemary isn't too pest- or disease-prone overall, but it is very sensitive to soil that stays too wet. Just keep monitoring the plant for watering needs if we experience any more dry spells or heat waves, and err on the side of underwatering a little bit if you're unsure if the plant needs water, since over-watering would potentially be more damaging. (Feel the soil about five inches deep next to the roots and water only when it's become fairly dry to the touch at that depth.)

Miri