A few other thoughts:
First, this could come from cable quality and/or length so I would also test with different cables. Remember that all cables are not created equal and you want to make sure you stay under 15ft for HDMI/DVI. If you use a DVI/HDMI amp, make sure your long cable is first then amp then short cable which is the opposite of analog amps.
Most LCD TVs have an HDMI input for computers which will behave different than the other HDMI inputs so make sure you test them all. .
As far as the Blackmagic devices, for some reason it doesn't always give you the right resolution in R4 but you still get it the right output. The best way to test is to create a 1920x1080 comp, show the test card, create a slice where both input & output are the whole area, select your BMD output and shift the slice one pixel at a time in X or Y position under Transform using the -/+ button. If your output is not getting the full resolution, you will see the 1-pixel vertical or horizontal lines appear and disappear. If these lines are moving across smoothly, then you're getting the right output even though it gives you the wrong resolution.