I was working with a client attending an institution that used Blackboard and there were no accessibility issues, per se, with Blackboard and JAWS 16.
I do have to say, though, that I don't think that anyone who relies on JAWS should have to go in to using Blackboard, no pun intended, blind. The system is wildly complex and the options within it that various instructors use can vary quite widely.
I pressured the institution in question to set up either a mock Blackboard system where individuals could practice using that or a couple of mock courses in their live Blackboard system that new students who are using any form of accessibility software for blindness or low-vision could be "enrolled in" so that they could practice navigating through blackboard before they had to do so in the context of taking a real course.
My feeling was that learning Blackboard with JAWS was quite akin to a full course in itself. The client I was seeing at the time was a very capable student but there was no way she was going to be able to deal with learning Blackboard and the actual course material at the same time.