Question
We have 2- 30yr old Japanese dogwoods, planted in the same area. They are shedding their lower bark and they also have some light green mold over the lower 2/3 of the trunk. Any thoughts as to what these problems are and any remedies for them?

Answer
Dogwoods do shed their bark as they get older. The green is more than likely lichens and will not damage the tree.
These are lichens and not a problem.
Lichens are organisms consisting of a fungus and a green or blue-green alga growing together in a mutually beneficial, symbiotic, relationship. The entire structure, called a thallus, is so different structurally from either of its partners that microscopic examination is necessary to distinguish the fungus and the alga.

The fungus obtains water and minerals from the air and the material it is growing on. The alga provides carbohydrates and vitamins. Some blue-green algae fix nitrogen that is used by both the alga and the fungus. Nitrogen is also obtained from bird excrement, organic debris, or plant leachate.

Lichens may be flat, leafy, or branched and hairlike. All three forms occur on tree bark as well as on rocks, soil, and other substrates. Colors may range from white to gray, red, green, yellow, and black.

Although lichens grow on tree bark, they are not parasitic (disease-causing organisms), and do not harm trees. The fact that lichens grow rapidly when exposed to full sunlight may explain their profusion on dead trees. The one conclusion that may be drawn with certainty from lichens on trees is that the air nearby is relatively pure. Most lichens will not grow in a smoky or polluted atmosphere

IF the tree is leafing out ok I would not worry about the bark or the lichens.  There are a couple of diseases that can damage dogwood trees but these all involve the branches dying back not the bark Unless the tree is dead. Wait until these leaf out this year and see what the symptom look like then and ask again at that time.