I've often been in meetings I wish I'd have recorded but didn't think about it until too late.
For that matter, I'd love the same concept with video, if there was a way to always record what I'm seeing without having to think about it in advance or wear a camera on my face, to capture anything interesting that happens to me, I'd be interested. I remember a story about an exec at Microsoft installing implants in his head for this purpose.
I'm terrified of anyone but me having access to this kind of data, though. It's nobody's business but mine.
Don't know about HeardApp, but I automatically assume the primary use case is for the company's benefit and not mine. Is it installing SilverPush on my phone and listening for things besides me to cross-reference and track my activity? I don't know...