I generated a WXR file using the Tumblr2Wordpress tool from Ben Ward (http://tumblr2wordpress.benapps.net/), and noticed that many of my recent posts were not imported.
The post_id's that that tool exports is Tumblr's unique numeric post ID, which as of mid-December eclipsed 2147483647, which is the 32-bit INTEGER limit.
The WordPress Importer on wordpress-importer.php line 434:
$post_ID = (int) $this->get_tag( $post, 'wp:post_id' );
It smashes whatever is specified as the post_id into an int. This causes a lot of nasty things to happen, specifically any further imports fail...
The wp_posts ID field is a bigint(20), which is much, much larger than PHP's (int), so that isn't the problem - at least at Tumblr's current post count ;)