Problems with pagination for a custom post type

1. Store your new WP_Query() in a variable
2. Globalize $wp_query
3. Move the $wp_query swap-hack to after your new WP_Query() generation
4. Pass the variable to $wp_query, not the new WP_Query() call itself.

e.g.

<?php 
// Custom query args
$press_query_args = array(
    'post_type' => 'press',
    'orderby'   => 'post_date',
    //'showposts' => '10',
    'posts_per_page' => $paged,
);
// Custom query
$press_query = new WP_Query( $press_query_args );

// Globalize $wp_query
global $wp_query;
// Swap-hack
$temp = $wp_query;
$wp_query= null;
$wp_query = $press_query;

// Output custom loop
while ($press_query->have_posts()) : $press_query->the_post(); 

// EVERYTHING FROM HERE BELOW SHOULD BE THE SAME,
// THOUGH I'VE CLEANED IT UP A BIT
// (MAINLY, REMOVING THE CLOSE/OPEN PHP TAG COMBOS)

// The following determines what the post format is and shows the correct file accordingly
$format = get_post_format();
get_template_part( '/lib/includes/post-formats/'.$format );

if($format == '')
get_template_part( '/lib/includes/post-formats/standard' );

endwhile;  

if (function_exists("pagination")) {pagination($additional_loop->max_num_pages);} 

$wp_query = null; $wp_query = $temp;
?> 

EDIT

Re: your pagination/post-per-page issue:

Hi chip, thank you, but this produces some odd behavior, on the first page you see 10 articles and then pagination from pages 1-7, but on the second page you get the first two articles that appear on page 1 and the pagination numbering changes to go from 2-35

I suspect the problem lies here:

$paged = (get_query_var('paged')) ? get_query_var('paged') : 10;

Couple with this array argument:

$wp_query->query(array( 
    'posts_per_page' => $paged,
));

What happens if you remove $paged and the 'posts_per_page' array argument?

ALSO:

The pagination (1-7 vs 2-35) issue is probably separate from the posts-per-page issue (though perhaps related). Try to use previous_posts_link() and next_posts_link(), just to isolate the posts-per-page issue.