I can't divulge our members IP addresses (I'm leaving out session information as well) for legal reasons but here is the relevant information from the error log:
message: Wrong value type sent to the database. Integer expected. (id_msg)<br />Function: MessageIndex
error type: critical
It looks like it is happening on this line:
array('id_msg' => 'int', 'id_member' => 'int', 'id_board' => 'int'),
array($modSettings['maxMsgID'], $user_info['id'], $board),
So it appears it has something to do with logging which boards have been seen.