Knowing the tv/film industry very well, I can give some strong background of what is going on. Initially, a friend showed me this video, knowing that I question everything before believing something.
My initial reaction was that it was not a green screen flub. Having used hundreds of green screen sets, this has never happened. A white/tan object opposed to a green backdrop or blue backdrop will not have severe spill to cause that. (Spill is when the backdrop casts its shade of light on the subject; which would have to be significant to cause his nose to become a part of the backdrop since it is not blue or green.) If it was a feathering mistake around the subject (this is kind of the "allowance" for how soft the computer-processed border is around the subject), then several other things would be turning invisible; as feathering encompasses the entire object in chroma keying. (Unless they literally chroma-keyed his nose separate from the rest of his body - but no person in their right mind/professional would ever do that.)
I guessed that it was likely caused by compression. When data is compressed, the least important information is essentially tossed out; while the key bits of data remain the same. This often results in clumping together of certain "unimportant" bits. Since neither subject was walking around or turning constantly, (and since his nose was a similar color to the white pole in the background) it's likely that the nose area would be affected by the compression. Which seemed to be confirmed when the post below showed the HD version of the video; where there is clearly no "disappearing nose."
Also, if my presumption was correct, it would mean that any significant motion, altering the nose+background combination, would actually result in some type of fading/disappearing of that portion of the nose. In other words, this would happen several times, not just once, if it was in fact a compression issue. Sure enough, I watched the highly compressed low-res version of this video, (https://www.youtube.com/watch?v=hEjLJFftuKI) and at 0:45 his nose disappears as the man walks down the stairs/woman walks up the stairs, 2:10 - the nose takes the color and curvature of the man's arm/black sleeve as he walks by, and 3:06 "the infamous nose turn" it happens as he turns his head significantly. Remember, a green screen's display is not part of the actual image until it is sent-to-out (the final product sent to output). If it were entirely a green screen video, then motion in the "background" would not affect the subjects ever, because that motion doesn't actually exist; only the output makes it "existent."
As for the shadows, no professional 3-point lighting setup (or better) would ever have visible shadows protruding from the subjects. This is what the "kicker" or "backlight" is for. It provides definition around the subject (mostly the hair) and eliminates shadows cast by the key and fill lights. Being a huge network with a national "reporter" (if you can call him that), it's likely that they had something even better than a 3 point lighting setup.
This is my professional summary of the interview. As much as I'd love for it to be "green screen" as they are so famous for doing, the facts do not lead to that conclusion. They overwhelmingly point to the "disappearances" as compression issues - solidified by the HD video. If you understand television production and technology, it truly does make this whole thing look silly. I will say, do not use this as an example of the media's lies; because in this case, the general public could easily prove you wrong, and attempt to discredit our movement.
I presented this info, as the Daily Paul has some of the most intelligent people on the internet - why? Because they study, research, and learn. You can look into what I said; so don't take my word for it; find out for yourself how green screen's work; so when it is green screen, you're not deceived. Every professional I know can point out a green screen immediately; via TV or Film. It's a very cool skill to have (or a buzzkill while watching movies, lol.)