Add the option to have an active recording going on but not actively saving every bit of the recording. Only have the recording save when I click a specific button, and it will "catch" the last 1 minute of audio and record that on the page I'm currently on.
I often find myself in lectures wanting to catch the last 30 seconds to 1 minute of what my professor said, but it's too late; they've moved on, and I can't start recording now because I missed it in the first place.

I got the idea from Steam gaming actually. Where it passively records the last hour of gameplay you've had but only saves the past minute when you specifically prompt it to. The 1 hour of the recording is kept for a day before it is deleted, leaving only the chosen recordings you want so you could modify the 1 minute you chose to be recorded.