There's no shortage of sci-fi stories dealing with this sort of always-on recording. "Strange Days", "Black Mirror (#3)". I wonder about the legality of this product, if it becomes inconspicuous.
Some product ideas:
1) "Datecast" -- get real-time advice and tips while on a date (or at a job interview. Or a business meeting -- is this startup's idea really that original? Or while shopping for some more complex consumer product: your remote wine expert suggests you to buy this particular bottle based on your previous tastes).
2) "Lifecast" -- our team of professionals reviews a total stream of your life and gives you advice on everything. They remind you how your wife liked this necklace a few days ago (you forgot, but they paid attention for you). That business meeting where you discussed your database scaling issues? An hour later we give you a call with with tips how to solve it. That hallway conversation? Transcripted before the next day.
3) Vacationcast: too old or poor or busy to go on a vacation? Want to relive your youth? Be anyone you want, transmitted in real time, unedited (this assumes that there's some thrill that seeing things happen real time, unscripted has over a more edited vacation footage). If video and audio alone is not enough, the vacationcasting company could offer a comfortable room, with scents and texture from your vacation destination.
4) Crimecam: anonymously send bitcoins to a criminal, encouraging a rampage of crime, broadcasted to your group of backers in real time. Will he get away with it?
Although, justin.tv has been doing this sort of thing for a while, and I'm not sure what has come out of it.