Yep. It’s busted in 3.1.2.
I should add that this is what my Default Page (page.php) looks like.
<?php get_header(); ?>
<br /><br />
<?php if ( have_posts() ) while ( have_posts() ) : the_post(); ?>
<?php the_content(); ?><br />
<?php wp_link_pages( array( 'before' => '' . __( 'Pages:', 'twentyten' ), 'after' => '' ) ); ?>
<?php edit_post_link( __( 'Edit', 'twentyten' ), '', '' ); ?>
<?php endwhile; ?>
<?php get_footer(); ?>