My tomato plants are covered with tiny, pill-like growths on their stems, pictured below. They're about 1mm wide and 3-4mm long, and they're widespread on both stems and branches. I'm also getting an early rot that turns my tomatoes brown, which may be related.
What is this, and how can I get rid of it?
These are the tiny hairs on the stems trying to turn into roots, above ground; they are called stem primordia, and this is usually caused by high humidity, over-watering or prolonged rain - see here.
Generally speaking, this is nothing to worry about, and is best ignored; however, it can be triggered by root problems or disease, and given that some of your tomatoes are rotting, it could be a bad sign and worth looking into - see Blossom End Rot - here.
