So, from those screenshots I can see that: 1) When you're not using the projector your output is 1360 x 768 (which is 16:9 widescreen). 2) When you are using the projector your output is 1024 x 768 (which is 4:3). So, even though your projected output (in the video) looked like it was widescreen, it must have been cropped (top and bottom), perhaps by the projector, to 16:9. I'm not sure what the best way to fix this would be. There may be some settings on the projector that allow you to use a 16:9 input signal, or perhaps some settings in the Display panel of the Mac OS X System Preferences. Another possible solution (and probably the easiest thing to do) would be to not make the output of MixEmergency full-screen, but to drag the output window onto the output screen, and then resize it to fit the 16:9 aspect ratio (so you'd want the output window to be 1024 x 576). Also, it looks like you have done this already, but I would recommend upgrading to MixEmergency 1.7 (which was released a week or two ago).
