I started having this issue today, annoyingly. I can’t tell which camera the blurry still is coming from. Unplugging and plugging back in the lightning cable is fixing it so far. I can verify it in Photo Booth before turning it on in Zoom.
I rebooted my Mac today and it started working, so that was the solution. Now it’s time for my unpopular opinion: It’s not that great. I don’t see the image quality as being much better than the much maligned camera on my Studio Display (it’s a bit better, but nothing spectacular). I’ll keep playing with it.
Out of interest, has anyone figured out a way to make the continuity camera work from the front camera instead of the rear camera? It looks like it isn’t possible, but I really think it should be!
I don’t have a third party webcam, and until the continuity camera function was ‘released’ I was using my MBP’s camera. This was very irritating because I prefer to have my MBP closed (I use an external monitor), and also because I hardly ever look like I’m looking at the screen because I’m looking at my external monitor. I hadn’t got around to buying a webcam, and also to be honest I just wasn’t keen on the additional software I might need to install.
Continuity camera therefore is a nice solution to a tech issue of my own making, but by only using the rear camera they’ve really restricted the functionality (for me). I have no issue with my phone being mounted all day (I’m using the Twelve South Hoverbar), but since I have to turn around the phone to use the continuity camera its use is severely limited. It requires “undocking” the phone and flipping it, which is stupid! If continuity camera could be set to use the front camera, all I’d have to do is rotate my phone 90° when I enter a meeting. In addition, because the phone has to be flipped to use continuity camera, I can’t see the screen if I get a notification!
I completely agree with @Bmosbacker’s comment about sometimes needing to send texts, I agree with @Jezmund_Berserker’s laughs about never using phones in meetings (some meetings are just that boring!), and I would also offer a third scenario I’ve been caught out twice with in the last week: 2FA during a meeting that sends a text to your phone… Twice now I’ve been unable to open a Google Doc shared during a meeting because 2FA was required and I couldn’t get the text due to using continuity camera (for those pondering, Google’s 2FA doesn’t show up on Mac’s iMessages, only on the phone). If it used the front facing camera, this wouldn’t be an issue.
So my view is: a good idea, poorly executed.
I do wonder if I’m just making life unnecessarily hard for myself and should buy a blooming webcam (which would have been cheaper than Twelve South’s stand 
).
I assume you can’t set your computer to get your 2FA and other notifications for some reason?
Apple makes that possible, so maybe the folks at Apple – and many/most of the enthusiastic beta testers? – have all those features turned on, so it may not occur to them during testing that this would be an issue