Categories and showposts? Can somebody check my code?

You’re using mixed array and string arguments in your query.
http://codex.wordpress.org/Function_Reference/query_posts#Passing_variables_to_query_posts

Try it with [untested]:

$temp = $wp_query;
$wp_query= null;
$wp_query = new WP_Query();
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
$args = array(
  'category__and' => array( 429, 1335 ),
  'posts_per_page' => 5,
  'paged' => $paged;
);

but when i load the page, nothing appears.

Do you see a blanco page, or does your layout appear, or do you see only posts from the first or second loop, or none. Do you have posts that have both these categories?

There are some errors (one is mine, sorry). Try it with this:

<?php
/*
Template Name: Medienecho
*/
?>
<?php get_header(); ?>
<?php get_sidebar();?>

<div id="content">

<div class="grid_8">
<div class="room">
<h2 class="h2">Aktuelle Diskussionsbeiträge</h2>
<?php
$temp = $wp_query;
$wp_query= null;
$wp_query = new WP_Query();
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
$args = array(
  'category__and' => array( 429, 1335 ),
  'posts_per_page' => 5,
  'paged' => $paged
);
?>
<?php while ($wp_query->have_posts()) : $wp_query->the_post(); ?>
<div class="grid_8">
<h4><a href="<?php the_permalink() ?>" rel="bookmark" title="Dauerhafter Link auf <?php the_title_attribute(); ?>"><?php the_title(); ?></a></h4>

<?php the_excerpt(); ?>
</div><?php endwhile; ?>

<div class="grid_8">
<?php if (function_exists('postbar')) postbar(); ?>
</div>

<div class="text grid_8">

 <?php wp_reset_query();
if( have_posts() ) : while( have_posts() ) : the_post();
 the_content();
endwhile; endif; ?> 

</div>
</div></div>
<div class="grid_4 kontakt">
<?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar("Seitenleiste Medienecho") ) : ?>
<?php endif; ?>
</div>
</div><!-- close #content -->
<div class="clear"></div>

<?php get_footer(); ?>

Yes i got posts of these categories.

Do you have posts that have both these categories, that’s what you’re querying for.

Try it with this:

<?php
/*
Template Name: Medienecho
*/
?>
<?php get_header(); ?>
<?php get_sidebar();?>

<div id="content">

<div class="grid_8">
<div class="room">
<h2 class="h2">Aktuelle Diskussionsbeiträge</h2>
<?php
$temp = $wp_query;
$wp_query= null;
$wp_query = new WP_Query();
$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
$wp_query->query('cat=429,1335&posts_per_page=5&paged='.$paged); ?>
<?php while ($wp_query->have_posts()) : $wp_query->the_post(); ?>
<div class="grid_8">
<h4><a href="<?php the_permalink() ?>" rel="bookmark" title="Dauerhafter Link auf <?php the_title_attribute(); ?>"><?php the_title(); ?></a></h4>

<?php the_excerpt(); ?>
</div>
<?php endwhile; ?>
<?php $wp_query = null; $wp_query = $temp; ?>
<?php wp_reset_postdata(); ?>

<div class="grid_8">
<?php if (function_exists('postbar')) postbar(); ?>
</div>

<div class="text grid_8">

<?php wp_reset_query();
if( have_posts() ) : while( have_posts() ) : the_post();
 the_content();
endwhile; endif; ?> 

</div>
</div></div>
<div class="grid_4 kontakt">
<?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar("Seitenleiste Medienecho") ) : ?>
<?php endif; ?>
</div>
</div><!-- close #content -->
<div class="clear"></div>

<?php get_footer(); ?>

http://codex.wordpress.org/Function_Reference/WP_Query#Category_Parameters