Yes I mean the ray depth limit for raytrace shadows, and also the max trace depth under raytracing in the render settings for mental ray. The last one should come to the sum of your reflections and refractions that you have set above. These are the two common things that will give you black glass as the rays shot out during raytracing are not getting through the surface properly.

When you get odd things like that patch it is usually some sort of strange reflection, a while back I was rendering a plastic ashtray and I got a similar thing to what you have there and I couldn't figure out why as I was rendering in isolation. As I moved the camera I understood that it was actually a reflection of the side of the ashtray that became detached at a certain angle and ended up giving this strange round patch at the center. So if this happens, the best thing to do is to move your lights or camera around a bit it usually fixes the problem and also tells you what caused it in the first place.

Glad to hear you're watching my lighting tutorial, geometry based light sources are very interesting to work with. One thing in your render at the moment, you have several lights with shadows turned on so the shadows are appearing in all directions. In most cases you only want one light to cast shadows as this is what will set a clear lighting direction in your scene so if you turn off the shadows for the other lights you'll see it will look a lot more realistic. Keep going, nice work so far