Issue in blender mesh composition import

Looks like it might be a manifestation of "smooth" edges.

When rendering models with Blender, you can specify which edges should be smooth or hard - this metadata is meaningless in Unity. Unity respects split edges; all joined edges will be rendered "smooth".

Within Blender, you must "split" those edges whose shading should not be smooth. In simple cases this can be done for you automatically with the Edge Split modifier, which splits edges based on their obliqueness.

Otherwise, this activity must be performed by hand. Remove any face which should be hard-shaded, but is currently sharing edges with adjacent faces. Re-construct this face, and do not issue the "Remove Doubles" command (which would undo what you've just done).

When I have to do this, I always make sure it's the last thing I do, as it limits many modeling conveniences. I also save a backup version, just in case I need to edit the model using those modeling features this operation prohibits.

There's an edit mode shortcut for separating / splitting the current selection (one or more faces), which is simply the "P" key. That can often save you from doing each face the long way.

Often you must take great care with your mesh topology. It isn't enough that it has the correct shape; it must also be constructed with realtime rendering in mind.