My problem indeed seems very similar to the one in the thread Signature verification failed, except I never once got that message (and therefore didn’t recognize it as a similar topic).
The advice from Lidwien that keeps coming back is to try and install the update for one partition, by putting it on the sd-card. However, I do have that file on the sd-card, but in Recovery Mode, the command line for Install from sc-card is completely empty: no files, no folders. And if I read correctly, the same goes for all the other with this problem.
I’m a bit miffed, because today I got a general mail saying that update 1.8.5 will be available from tomorrow (?!) and includes a pre-update of the installer. Since my installer hasn’t worked well for ages, I didn’t realise that the manual install files went out ahead of the general update. I am kinda sorry I updated to one partition now, if I had just stuck with 1.8.5 but without the one partition update, I might have had problems with storage for apps, but at least I would have still had them… Perhaps when the update is added to the installer tomorrow it will do some good for us. I’m crossing my fingers.
EDIT: @Therob: the google app store installation does indeed run from within the installer now, so that much has changed, but it doesn’t actually work.