I'm trying to model a polished material with mirror like properties (shiny new body of car).  My specular reflections use fresnel schlick approximation but I noticed the reflections were kind of dim.  After investigating I see why:

Suppose I have a flat quad and the view ray strikes the surface normal N at 45 degree angle, and the reflection vector R intersects a light source with light vector L.  With classical specular function, we would do some formula like dot(L,R)^m and the above configuration would give a maximum specular contribution.  This result gives me what I would expect.  But with fresnel schlick, we look at (1-dot(R, N))^5 = (1-.707)^5 which will be small number, thus resulting in the dim specular.  

Of course this makes sense for what we intuitively expect fresnel to do (increase reflection at glancing angles and more refraction/diffuse when looking head on), and it works well for things like water/glass, but it does not seem to be working well for modeling the shiny car.  However, my understanding of PBR is that everything should use fresnel.  Is there a flaw in my understanding?  If it helps, I'm using fresnel F0=(0.04, 0.04, 0.04) which real-time rendering suggest for plastic/glass.

Schlick fresnel should work fine for the clear coat surface of a car. The clear coat basically acts like a layer of clear plastic/glass over the paint, so the same rules apply. Perhaps your light source isn't bright enough? You should also make sure that your specular terms are properly balanced with your diffuse terms. For instance if you omit the 1 / Pi in the Lambertian diffuse BRDF, then your specular will always look too dim (since your diffuse will be too bright).