###結論：svn/dav, svn/dbの権限変更が必要
下記の二つのDIRにapacheを動かしているユーザにオーナー権限を与えます
/usr/local/svn/dav #activity databaseというものらしい
/usr/local/svn/db #transactionログなどか

shell>>

chown www-data:www-data -R /usr/local/svn/db

chown www-data:www-data -R /usr/local/svn/dav

<<--

###エラーの内容など
shell>>
$svn ci -m "test"
svn: Commit failed (details follow):
svn: Can't create directory '/usr/local/svn/db/transactions/1128-1.txn': Permission denied
<<--

→ chown www-data:www-data -R /usr/local/svn/db

shell>>
$svn ci -m "test"
svn: Commit failed (details follow):
svn: Can't open activity db: APR does not understand this error code
<<--

→ chown www-data:www-data -R /usr/local/svn/dav

###Refs
http://svn.haxx.se/users/archive-2005-10/0084.shtml
http://svn.haxx.se/users/archive-2004-02/1350.shtml