I have realized in my short time here that I will get flamed for this, but I, too, did the Blue Hole as an inexperienced diver. However, I think I was partially aware of the limits of my abilities and fully aware of what it's like to experience equipment failure (see my OW incident thread). I just want to give some insight to my experience and I think that many of the operators take care to make the dive as safe as possible.
I approached a couple of dive shops about the dive after I received my OW certification asking whether or not it would be appropriate for me to dive the Hole. Each of them told me that it would most likely be fine but I should try to get some deeper dives to see how I would react. If I was fine after going to 80-100 ft I should be fine. Many of the dives outside of the reef on the cayes of Belize are typically 80ft. or more. So I did a few of those and all was well. I ended up going with a shop who knew full well I had been certified a few days before and said they took the appropriate precautions for new divers.
So we get out to the dive site and they cut the motors, gathered everyone together and gave us a good 10 minute dive briefing. Went through hand signals, what to do if you couldn't clear, what to do if you got narc'ed, talked about the deco station under the boat, etc. Then they split the group into experienced and inexperienced divers. We had about 8 divers with us (the inexperienced ones) and they sent 2 DM's (one to lead and one to tail). When we descended we stopped at the reef to regroup where 2 of the divers were sent back to the boat (we found out later that the DM was not comfortable taking them down). We descended the rest of the way which was somewhat anticlimactic given the lack of a reference point on the bottom. We hit 135 before we knew it, swam just inside the first row of stalagtites/mites (the more experienced group went further in) and then started a slow swimming ascent along the wall. We were covered by the DM's the entire dive, they were constantly checking air and status, and we all made it through. We also happened to get circled by about 10 reef sharks at the deco stop which was pretty impressive.
All in all I felt safe. There was an unknown factor with the depth (never been that deep, didn't know how I would react) but I felt like we had sufficient coverage. I later found out (over beers, after the dive) that they know that they "technically" should not take newbies down that deep but the simple fact of the matter was that there is a market for it and if they don't do it, others will. But they felt they had a very good system with an excellent safety record and that's why they do it.
Ok- that's all I have to say. I am donning my fire suit now.