Adding to what Peelman said (as I can't comment on his answer), for me, adding the --config-dir directive to the subversion_adapter.rb file was the final piece of the puzzle (i'd tried various ways of running svn and permanently accepting the certificate, but redmine wouldn't find the config).
To clarify, the complete steps were:
1: Modify Redmine's subversion adapter script
# pico /usr/share/redmine/lib/redmine/scm/adapters/subversion_adapter.rb
Change the line in that file with command line args
str << " --no-auth-cache --non-interactive"
str << " --config-dir /usr/share/redmine/svn/.subversion --no-auth-cache --non-interactive"
2: Ensure subversion client accepts the self-signed cert permanently
# sudo -u www-data svn --config-dir /usr/share/redmine/svn/.subversion list
When prompted, select the option to accept certificate (p)ermanently
To complete the test, enter your subversion credentials when prompted (hit enter at the first username prompt for www-data and it'll ask again for another username). When prompted select "no" to saving your credentials unencrypted (the necessary acceptance of the SSL cert has already been saved by this point). You can verify that by looking inside the /usr/share/redmine/svn/.subversion directory, where you'll find a directory called svn.ssl.server with a new file in it.
Obviously if your copy of redmine runs as a user other than www-data you should sudo using that user instead. Make sure the user you sudo to has the necessary permissions to create an /svn directory inside the redmine directory - otherwise you may not be given the option to (p)ermanently accept the certificate when you run the svn client.
3: Restart Apache
In my case, redmine is running using mod_passenger under apache, so it was necessary to restart apache to pick up the changes to the redmine subversion adapter script (prior to the restart I was still seeing errors in redmine).
# /etc/init.d/apache2 restart
4: Browse to a project's /repository in Redmine
Everything should now be working