I am currently using App release 26, FW 1466836533
I was curious on your problem, so I tried it with the exactly same OAD results as you. So I agree something is wrong with the new firmware updating code. I was able to “continue without updating” and it seems to working with the new App 27 with the older firmware 1466836533.
Since you say you are on FW 1462564395 now, (that was bundled with App version 22), you are certainly missing a lot of good changes James has made. Unfortunately the Playstore only allows you to install the latest version, so I’m sure James will want to fix this soon. In the meantime, you can always download previous released versions from here https://github.com/mooshim/Mooshimeter-AndroidApp/releases. Release 26 is pretty stable and it has included FW 1466836533. Hopefully you know how to side install apps from unknown sources.