Very nice work. I just have two concerns:
1- I agree with the nail issue. If you are going to attach it to the wall by the back, you really need something better than nails holding the back to the cabinet. Like you said, it is holding $3000 worth of collectibles, plus you put a lot of work into the cabinet. Do you really want to have any doubt about whether or not the cabinet will pull away from the back?
2- From some of your earlier posts, I think you said the back is 1/4" thick. Now, I wouldn't be concerned about this (or the nails) if you weren't using the back to hold it to the wall. Once again, it will be vulnerable to being pulled away from the wall, either by the screws tearing through the holes, or by the back simply breaking.
I don't think anything would happen just from hanging on the wall. But, if something unexpected happened, the attachment of the back to the wall and the rest of the cabinet would be the two weak links.
Since the cabinet is done, you may want to consider adding hardwood strips behind the cabinet where you are screwing into the wall and screw them into the frame of the cabinet. You will have to consider whether or not you like the aesthetic effect, or add trim to hide the strips. You may also be able to take advantage of the blocks at the top. If they are well connected to the frame, you could screw through them into studs. This would make for a much more structurally sound attachment method.