Untick sim objects cast shadow unless you want buildings etc to cast shadows. You'll notice there are two shadows columns. One for projecting a shadow and one for receiving a shadow. Check the box Terrain receive shadows and and leave the other unchecked. Also increase the resolution on your terrain mesh. I'm having the same issue and this has reduced it by quite a bit. The shadows which control whether your aircraft casts a shadow and receives a shadow are controlled by the first two options in the shadows settings make sure all four boxes are checked. I have those and terrain receive shadow checked and that's it. It's a little buggy still. Also you might want to turn off cloud shadows in your p3d.cfg file.
OR -- you can simply wait and upgrade to version 2.2 which should be released soon which addresses shadow issues among other things.
