I checked here and it mentioned that the built-in Vino does not have logging:
http://ubuntuforums.org/showthread.php?t=1077704
Then it mentioned to check the auth.log and these are the last entries after I tried to use UltraVNC (I got the "VNC" app from your market installed on my HDA):
May 22 07:55:41 monster dbus[923]: [system] Rejected send message, 2 matched rules; type="method_call", sender=":1.34" (uid=1000 pid=3284 comm="/usr/lib/telepathy/mission-control-5 ") interface="org.freedesktop.NetworkManager" member="GetPermissions" error name="(unset)" requested_reply="0" destination="org.freedesktop.NetworkManager" (uid=0 pid=971 comm="NetworkManager ")
May 22 07:55:41 monster dbus[923]: [system] Rejected send message, 2 matched rules; type="method_call", sender=":1.47" (uid=1000 pid=3663 comm="/usr/lib/ubuntu-geoip/ubuntu-geoip-provider ") interface="org.freedesktop.NetworkManager" member="GetPermissions" error name="(unset)" requested_reply="0" destination="org.freedesktop.NetworkManager" (uid=0 pid=971 comm="NetworkManager ")
May 22 07:58:10 monster su[2627]: Successful su for achmetinternet by root
May 22 07:58:10 monster su[2627]: + ??? root:achmetinternet
May 22 07:58:10 monster su[2627]: pam_unix(su:session): session opened for user achmetinternet by (uid=0)
May 22 07:58:10 monster su[2627]: pam_unix(su:session): session closed for user achmetinternet
May 22 07:58:11 monster dbus[923]: [system] Rejected send message, 2 matched rules; type="method_call", sender=":1.32" (uid=1000 pid=3189 comm="nm-applet ") interface="org.freedesktop.NetworkManager" member="GetPermissions" error name="(unset)" requested_reply="0" destination="org.freedesktop.NetworkManager" (uid=0 pid=971 comm="NetworkManager ")
May 22 07:58:11 monster dbus[923]: [system] Rejected send message, 2 matched rules; type="method_call", sender=":1.34" (uid=1000 pid=3284 comm="/usr/lib/telepathy/mission-control-5 ") interface="org.freedesktop.NetworkManager" member="GetPermissions" error name="(unset)" requested_reply="0" destination="org.freedesktop.NetworkManager" (uid=0 pid=971 comm="NetworkManager ")
May 22 07:58:11 monster dbus[923]: [system] Rejected send message, 2 matched rules; type="method_call", sender=":1.47" (uid=1000 pid=3663 comm="/usr/lib/ubuntu-geoip/ubuntu-geoip-provider ") interface="org.freedesktop.NetworkManager" member="GetPermissions" error name="(unset)" requested_reply="0" destination="org.freedesktop.NetworkManager" (uid=0 pid=971 comm="NetworkManager ")