Whenever the game transitions from one scene to the next. My screen goes black and I have to press alt-tab to bring it back. When alt-tab is pressed it looks like there are two instances of the game up. Selecting one takes it back to normal until the next transition. Any ideas how to fix this?

If a video should play between the scenes, it's a pretty well known problem of KOTOR, try to select "Disable Movies" option in swconfig, in the game folder

Also try to launch the .exe directly without the gog launcher

It's a known problem (as stated) that has to do with the .bik movies used in newer operating systems. Another way of mitigating the annoying problem of being dumped back to the desktop during or after cut scenes, is to switch to windowed mode when you know they are coming, and switch back afterwards -- the game shouldn't dump you out while in windowed mode. To do this, simply press ALT+ENTER, and the same to go back to full screen. It's a pain, but it's better than having to shut the game down with task manager.