Gordon,
It looks like you made the same mistake -- twice... Easy mistake to make -- also easy to fix.
When you create a wing, you really define the right (positive Y) wing. Since most models will have a symmetrical wing copy, we turn on XZ symmetry for wings by default.
For a vertical tail, you rotate about the x-axis by 90 degrees. Since the vertical is still on the center line (y=0), you end up with two vertical tails perfectly superimposed on top of one another.
This really confuses the geometry generation before VSPAERO -- causing the mixed color triangles in the GUI and also the missing gaps you see later in the VSPAERO viewer.
Other geometry types don't have symmetry enabled by default. However, at some point, you enabled symmetry for the fuselage. Since the fuselage is sitting on the center line, you ended up with two fuselages perfectly superimposed again -- causing the same problems.
So, turn off the symmetry on the vertical tail and the fuselage and you can get this solution...

You will certainly want more spanwise resolution, but with some experimentation, you should be able to get good results.
Although symmetry threw off your vertical tail and fuselage, it would be good to use it for the actuator disks and engine pods. You used blank components and attachment to make those assemblies (good), so when you use symmetry, you need to choose an ancestor axis to be symmetrical about... There was a presentation at the 2016 OpenVSP Workshop about symmetry and attachment. That is probably the best documentation available on that.
You threw me off of the 'control group' discussion because the setup configuration window is on the right -- the current GUI doesn't do anything for control surfaces.
The version of VSPAERO you are using can model control surfaces when running in the thin-surface VLM mode. Control surfaces can be grouped to model coordinated surfaces, mixing, etc.
Soon, the OpenVSP GUI will be modified to allow definition of control surface groups without editing the control file manually.