Google Realtime is a dual functioning tool which lets you watch tweets as they come through (live) but also allows you to scroll backwards and see tweets from as far back as March 2010. Not bad at all.
Hopefully, a video mp4 thing that I created with Screencast-O-matic (it's free) will appear below. I've checked the sound and it's perfectly listenable with the volume up a bit but it's not perfect. I'm embarrassed to admit I don't know where the microphone is on my new mini laptop... oops.