What are some good Shade/Part-Shade edible plants?
You can try currants for edible fruit.
Alpine strawberries will take quite a lot of shade, and it will help keep the plants in better condition in hot climates.
Regular strawberries will grow in partial shade, but will not fruit as well as they do in at least a half-day's sun. I've used day-neutral strawberries to replace vinca under an ash tree, and they work pretty well (but aren't my main strawberry source).
Serviceberries are actually an understory tree, and do just fine in the shade of a building or a much taller tree.
The next one is my personal view, but I find that the best blackberries come from plants which are growing in the shade, if only because the ground is more likely to stay moist. The slower ripening also means that even wild berries get plump before they ripen.
Most mints are shade-tolerant, up to a point, but need good air circulation to ward off disease.
In general, leafy edibles (lettuce, other tender greens, parsley) do better in shade than fruiting edibles, and may even need some shading to permit a summer harvest in hot climates (which seems to be most of us now).
Ostrich fern for spring fiddleheads.
Solomon's seal grows nicely in full or part shade and the spring shoots are reported to be usable very similarly to asparagus. By one account in the book _Perennial Vegetables_, even preferable. The giant Solomon's seal variety (Polygonatum biflorum var. commutatum -- synonyms: P. commutatum, P. canaliculatum, P. giganteum) is more convenient for eating purposes because the shoots are much thicker than the standard smaller version. You'd have to pick quite a few of the smaller ones to contribute usefully to a meal since their shoots are pencil thin or maybe thinner.
Other shade-tolerant listed in _Perennial Vegetables_ include ramps, fuki (aka butterbur), and wood nettles. The uncooked nettles, sadly, sting if touched, so would have to be located and treated with care. The book includes still others, but I haven't read through it with care outside of the plants that are suited to my colder climate.
An article at http://hubpages.com/hub/Shade-Gardening-101 on shade gardening also lists ginseng, highbush cranberry, sumac (for 'pink lemonade' sun tea made from the fruits--other parts are poisonous).
And then there's mushrooms, which can be cultivated on inoculated logs or in some mulches. Oysters, chicken of the woods, hen of the woods, and so forth.