I’m pretty sure you know about the “Network may be monitored”-“bug”, as you wrote about it in the FAQs. For me this thing is pretty annoying and i am sure, android won’t be changed back again, so i dislike the way DAVdroid needs to handle self-signed certificates (Don’t get me wrong, from a developers pov, this is the best suited solution! But it is annoying for the user).
As the usage is nearly impossible for a non-IT-guy, i’d like to suggest to handle those certificates like several other applications (for example owncloud): Make it possible to import the certificate in the creation of an account.
I searched in the owncloud app, how they do it, and it looks pretty simple to me: https://github.com/owncloud/android/blob/master/src/com/owncloud/android/ui/dialog/SslUntrustedCertDialog.java