Index: wp-admin/admin-header.php
===================================================================
--- wp-admin/admin-header.php	(revision 18488)
+++ wp-admin/admin-header.php	(working copy)
@@ -139,9 +139,13 @@
 
 <img id="header-logo" src="<?php echo esc_url( includes_url( 'images/blank.gif' ) ); ?>" alt="" width="16" height="16" />
 <h1 id="site-heading" <?php echo $title_class ?>>
-	<a href="<?php echo trailingslashit( get_bloginfo( 'url' ) ); ?>" title="<?php esc_attr_e('Visit Site') ?>">
+	<?php if ( !is_network_admin() ) { ?>
+		<a href="<?php echo trailingslashit( get_bloginfo( 'url' ) ); ?>" title="<?php esc_attr_e('Visit Site') ?>">
+			<span id="site-title"><?php echo $blog_name ?></span>
+		</a>
+	<?php } else { ?>
 		<span id="site-title"><?php echo $blog_name ?></span>
-	</a>
+	<?php } ?>
 </h1>
 
 <?php
Index: wp-includes/admin-bar.php
===================================================================
--- wp-includes/admin-bar.php	(revision 18488)
+++ wp-includes/admin-bar.php	(working copy)
@@ -101,7 +101,7 @@
 function wp_admin_bar_dashboard_view_site_menu( $wp_admin_bar ) {
 	$user_id = get_current_user_id();
 
-	if ( 0 != $user_id ) {
+	if ( !is_network_admin() and ( 0 != $user_id ) ) {
 		if ( is_admin() )
 			$wp_admin_bar->add_menu( array( 'id' => 'view-site', 'title' => __( 'Visit Site' ), 'href' => home_url() ) );
 		elseif ( is_multisite() )
Index: wp-includes/class-wp-admin-bar.php
===================================================================
--- wp-includes/class-wp-admin-bar.php	(revision 18488)
+++ wp-includes/class-wp-admin-bar.php	(working copy)
@@ -98,12 +98,14 @@
 				</ul>
 			</div>
 
-			<div id="adminbarsearch-wrap">
-				<form action="<?php echo home_url(); ?>" method="get" id="adminbarsearch">
-					<input class="adminbar-input" name="s" id="adminbar-search" type="text" value="" maxlength="150" />
-					<input type="submit" class="adminbar-button" value="<?php _e('Search'); ?>"/>
-				</form>
-			</div>
+			<?php if ( !is_network_admin() ) { ?>
+				<div id="adminbarsearch-wrap">
+					<form action="<?php echo home_url(); ?>" method="get" id="adminbarsearch">
+						<input class="adminbar-input" name="s" id="adminbar-search" type="text" value="" maxlength="150" />
+						<input type="submit" class="adminbar-button" value="<?php _e('Search'); ?>"/>
+					</form>
+				</div>
+			<?php } ?>
 		</div>
 
 		<?php