After I wrote up my post about problems changing my Ubuntu’s user account password, which didn’t automatically updated Gnome’s keyring, I found that I was not the only one suffering from this problem.
A while ago I upgraded to 10.04, and not long after that I had to change my password again (the half-yearly password-will-expire-soon emails started coming in on the account I use on that system). So I did. With that I can also confirm that the keyring password problems have been fixed by the Ubuntu team in 10.04.
Thanks Ubuntu!