I've now got my Thunderbolt to HDMI adapter and I've tried my Mac Mini out on three different monitors. One thing I've noticed is that display calibration is completely inconsistent between the two outputs. What looked perfect on one looks like crap on the other. Re-calibrating for that output (creating its own preset) solves the problem, but one can't help but wonder what's going on internally in the display hardware that they are so far off from each other.
One one of the monitors I tried, it's also a TV set (Insignia TV/Monitor) and it had default settings in its own menus that were horrible for being used as a computer monitor. I had to turn off the TV's overscan for the HDMI Input #1 (which then forces OSX to use underscan to fit the screen which results in scaling which makes font edges look awful). I had to change the color to "normal" (it was default set to 'warm' which screws with colors) and I had to turn sharpness down to ZERO since anything above that makes bloom (think 'white shadows' around text). Calibrating then in OSX with ADVANCED mode (regular mode still didn't look right at all; too saturated) resulted in a good looking picture from either output, but the calibration had to be done for each separately. My LG monitor needed relatively small calibration (no advanced needed to get a good picture) by comparison and the AOC monitor needed advanced, but not as severe calibration as the Insignia. Needless to say, I'd rate each monitor's quality over the years in that order (LG->AOC->Insignia).
I can't help but wonder if SOME (I can't dismiss other GPU issues on specific machines) of the people getting "bad pictures" but no more blackouts or flickering simply need to recalibrate their displays and perhaps using advanced as well. The difference between flat-screen monitors is HUGE in this regard and as I said, the output is different between the HDMI and Thunderbolt/DP outputs on the Mac Mini. That doesn't mean both can't get the same picture on any given monitor. They simply need their own calibration settings for any given monitor.
Two other things that can wreak havoc on picture quality are not using the native display resolution (forces scaling which as I said above can either create jagged edges or blurry/soft text). In Mountain Lion, the "Best For Display" normally picks the monitor's native resolution (Snow Leopard or earlier needed you to pick the correct resolution manually, I believe). Also, you need to make sure that "Use LCD Font Smoothing When Available" is checked in the GENERAL Preference Pane or fonts won't looks as good on LCD/Flat-screens as they would on older CRT monitors.
The "snow" that appears on waking from sleep or other situations is definitely HDCP hand-shaking. I've seen it on other devices on HDTVs several times now and so it's nothing to do with anything in the Intel 4000 chipset. Some monitors might not lock properly all the time (My LG seems to have more issues than my AOC, which always locks instantly every time). Personally, I've had zero blanking screens (never had the flashing ones) since the firmware update and so as near as I can tell, the GPU is now working correctly and I can verify both outputs produce fine looking displays (although again, they need independent calibration for a given monitor if you're testing both out on one monitor).
Edit: After switching outputs after configuration, it appears the output IS the same, after all on both outputs. I'm not sure why it appeared to be so different when I first swapped outputs. But the calibrated output I did after that point worked well on both outputs for the same monitor. Certainly, trying to get both monitors (of different brands) to look the same (or even very similar) is far more difficult, but this is independent of output. Everything else I mentioned above still applies, however.