Redirect logged in user to somepage on every page view?

I would utilize the user meta info and ‘wp’ hook for this. You can use a function similar to below:

add_action( 'wp', 'wpse69369_special_thingy' );
function wpse69369_special_thingy()
{
    if ( is_user_logged_in() && "" == get_user_meta( get_current_user_id(), 'completioncheck', true ) )
        wp_redirect( string $location ); 
        exit;  
    }
}

Then when the user completes the action necessary you can use the following function:

add_user_meta( get_current_user_id(), 'completioncheck', 'yes' );

Info on the user meta functions I used can be found here:

get_user_meta()

add_user_meta()