Leaves fall off something, so that something must be referred to, explicitly or impliedly - so "There's something wrong with those trees: the leaves are falling off" is OK. If we haven't been talking about trees or plants, and you say, "The leaves are falling off", I will think, "Falling off what? The trees? My blackberry bush? My hemp plant hydrangea?"
Oddly enough, if you just say "The leaves are falling," I think most people would take it to mean that they are falling off the trees (especially if it's autumn), whereas the word "off," to me, introduces the problem that sound shift discusses above.