(Legal Disclaimer: Despite the fact that this question was asked of me recently and I did give an answer, what follows is the beginning of a wider analysis of the sources that deal with head covering. It is meant to provoke discussion, not to render any sort of decision.)
Question: "I have a Skype interview tomorrow. Since I am technically in my house, do I need to cover my hair? (I cover if men are expected in the home, but not in front of other women, or children...)"
Response: There is a certain ambiguity inherent to video-conferencing. As in your situation, your "person" is in the West, but your image and voice may be seen a thousand miles to the East. The same may be said of your potential employer, his or her "person" is the East, but the individual's voice and image carry to a computer screen in the West.
So where is the interview said to occur? Shall we say that you are sitting in your potential employer's office? Or shall we say that your potential employer is sitting in your dining-room or den?
Perhaps we might say that it is an in-between zone. A physical parallel of this 'virtuality' might be one's front porch or gated lawn...you are not exactly in your home, but you are not exactly in the street either. (In due time, I shall discuss the "Courtyard" scenario in Ketuvot 72a/b as well as Rav Henkin's discussion of the latter in B'nei Banim III.24)
Alternatively, one may object to the whole premise of the question: Why should photographs and videos be given any legitimacy. At the end of the day, 'they show a body without a soul...' Must a woman cover her hair every time her daughter decides to snap a photo of her (or shoot a video of her) with an iPhone or similar device? The technological repercussions of stringency might (and may in fact already) straight-jacket women into keeping their heads' covered even in their own homes among family, lest an unruly teenager snap a photo and post it on Facebook...
To be continued...