Did you execute the normalization procedure and those tables remained unchanged?

Safely convert the encoding is what that procedure is supposed to do.

@mgsolipa I've tried running that several times. It appears to report everything as having been completed successfully, but when I try to-rerun the installation, I get the same message about those two tables. Looking at phpMyAdmin just confirms that those two tables are set to the 'latin1_swedish_ci' charset - something I'd never have chosen for myself, I'm kind of stuck with English only for my sins.

This has been answered at least 5 times already :p

Uninstall the captcha plugin and re-install it. (Some newer version is supposed to fix this but apparently it's not in the version you use. Did you really not use 6.6.5 ??? )

I don't know what your other plugin is but a similar treatment might work.

Alternatively, you can change the charset directly in PhpMyAdmin.

I got my version numbers wrong in my original post - it is the latest one I tried upgrading to.

The test install was a copy of the one I did have on my live hosting, complete with data, from quite a few months ago. I thought I'd try the auto upgrade on it, but without much success.

It's not happy in its current state, so I can't disable the Captcha plugin - so long as I can fix it in phpMyAdmin safely, I'll do that and run the install again.

I got the charset sorted and seemingly, the install ran OK. What I've ended up with though, is a back-end that works correctly, but the front-end doesn't. That now looks like this. Any suggestions?

It's fixed now. Something obviously went wrong with the skin. I cleared it all out, and re-uploaded it from a clean copy - it's working again.