It might be something in accounts.ini. Try renaming it really quick (while Opera is closed of course). Put it back if that doesn't help.
Also, try just renaming the whole mail folder. If the probably doesn't go away then, it's a problem outside of the mail folder.
Does Opera Mail put anything in the registry
if so, will that be cleaned up by the uninstall?
Some stuff will be. Stuff that remains shouldn't be a problem.
Been playing around with Opera Mail, testing some import scenarios.
Just delete "C:\Users\John\AppData\Local\Opera Mail\Opera Mail\mail" (and optionally contacts.adr, wand,dat and operaprefs.ini in "C:\Users\John\AppData\Roaming\Opera Mail\Opera Mail" while Opera is closed. When Opera Mail starts up, you'll get the import dialog. That's all you need to do really. You don't even need to uninstall Opera Mail and reinstall it (unless you want to fix Opera Mail registry settings). And, when the import dialog pops up this time, if you have Opera 12.16 installed to "C:\Program Files (x86)\Opera" and it's the default browser, you'll get a new import option that copies the whole mail folder, contacts.adr, wand.dat and operaprefs.ini from 12.16 over to Opera Mail so that all your mail and settings are restored.
Am I missing anything?
You got the idea just fine. Although, it's a little overkill for what you're trying to accomplish. But, it'll do the trick just fine.
Note that those "Opera Mail" folders contain a folder for each Opera Mail you have installed. For example, if you have "C:\Program Files (x86)\Another Opera Mail", you'll have "C:\Users\John\AppData\Local\Opera Mail\Another Opera Mail" and "C:\Users\John\AppData\Roaming\Opera Mail\Another Opera Mail" folders. As you can see, the names of the profile folders in those Opera Mail folders are based of of the program files folder names. So, really, you only need to delete "C:\Users\John\AppData\Local\Opera Mail\Opera Mail" and "C:\Users\John\AppData\Roaming\Opera Mail\Opera Mail" if you want to clear the profile for "C\Program Files (x86)\Opera Mail".
operaprefs_default.ini, not just operaprefs.ini. Should that one exist?
operaprefs_default.ini is for global options. It's not a file that you usually mess with. operaprefs.ini is for user options and is the one you should mess with.
Is there any documentation on other options we can tweak in that INI file?
Download Opera 12.16, launch the installer, click "options", change the "install path" to a folder on your desktop (or somewhere else in your user profile area), set "install for" to standalone installation", and install. Then, launch it, type opera:config in the address field and press enter. opera:config is a front-end to operaprefs.ini. In operaprefs.ini, there's a '?' next to each setting. If you click it and there's info on that setting, it'll tell you.
Since Opera Mail is just Opera 12.16 with the browser parts mostly hidden, you can use almost all of the same settings in operaprefs.ini.
Also, see http://shadow2531.com/opera/wiki/How to Add opera config to Opera Mail - Mail Client ( M2 ) - Opera Wiki.mhtml (download and open it in your browser or just open it in Opera 12.16) to see how to add opera:config back to Opera Mail (in the english version of Opera Mail at least).
There used to be an opera-provided page for explaining all the settings. But, it's gone and there's just http://help.opera.com/operaconfig/versions/Win32/11.00/en/index.html in an unformatted state.