For myself I went the extra mile to just have my laptop record ALL audio but then felt this was a little too douchey/NSA-y and disabled the whole thing and wiped the audio. I wanted such a system not only for "You said this then and now you are saying that now" but to remember things I had said myself. I wanted to hook it up to STT to have a searchable archive of what I had said but again it was an invasion of privacy (to people around me) that I personally couldn't stomach.
You'll be happy having the audio even if there are restrictions. Simply don't tell anyone about it until the benefits (saving your ass) outweigh the drawbacks (potential charges).
As for you, there's nothing morally wrong in wanting to not be trapped by a liar. And it doesn't magically become morally wrong if you walk into a two-party state.
Transcribing audio to text
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...
This is by far the biggest problem with this kind of tech. If there were a way to guarantee the privacy of the recordings, it would be a super useful tool. You could basically have a perfect photographic memory. Not to mention all the cool processing you can do with the data. The idea really excites me, but equally terrifies me.
But I think given enough time and progress in encryption/speech recognition/legal issues, I think something like this is inevitable. It's hard to see a future where we record less. I think another key part is having access to data of you. That way you don't feel like it's being recorded to be used "against" you.
I'm guessing your phone would have to be pretty close to the child though.