A few people have run into this, but unfortunately (again) I'm not one of them. I routinely run the application on 3 different PCs and 6 or so virtual machines, and I've never run into this issue. Like I believe I've said before, it could be a memory issue, with the most likely culprit being the changing of screens in the main window. If your layout does that a lot, I highly recommend reducing the frequency of screen changes until the next beta of 3.4 is ready (3.4 beta 3), where I've reduced the memory footprint associated with screen changes. If that's not the case for you, then unfortunately at this time I don't know what is causing the issue.
To be clear, sometime after IE 11 was released all of the PCs on which I run the application did start to display similar behavior, where dialogs opened black, but the behavior was different in that the black color was only very brief. Some dialogs open black but quickly they render the expected way, so you only see black for a split second. And certainly the app hasn't crashed with black screens or dialog windows. (For me anyway.)
It could be a newer version of mshta, which is the container for the application. The next beta will include an older version of that container. Maybe that will help. (Maybe only wishful thinking, too.)