Index: wp-includes/admin-bar.php
===================================================================
--- wp-includes/admin-bar.php	(revision 19687)
+++ wp-includes/admin-bar.php	(working copy)
@@ -75,7 +75,7 @@
 	$wp_admin_bar->add_menu( array(
 		'id'    => 'wp-logo',
 		'title' => '<span class="ab-icon"></span>',
-		'href'  => admin_url( 'about.php' ),
+		'href'  => is_network_admin() ? network_admin_url( 'about.php' ) : admin_url( 'about.php' ),
 		'meta'  => array(
 			'title' => __('About WordPress'),
 		),
@@ -87,7 +87,7 @@
 			'parent' => 'wp-logo',
 			'id'     => 'about',
 			'title'  => __('About WordPress'),
-			'href'   => admin_url('about.php'),
+			'href'  => is_network_admin() ? network_admin_url( 'about.php' ) : admin_url( 'about.php' ),
 		) );
 	}
 
Index: wp-admin/includes/update-core.php
===================================================================
--- wp-admin/includes/update-core.php	(revision 19687)
+++ wp-admin/includes/update-core.php	(working copy)
@@ -601,7 +601,7 @@
 /**
  * Redirect to the About WordPress page after a successful upgrade.
  *
- * This function is only needed when the existing install is older than 3.3.0.
+ * This function is only needed when the existing install is older than 3.3.0 (3.4.0 for multisite).
  *
  * @since 3.3.0
  *
@@ -609,8 +609,13 @@
 function _redirect_to_about_wordpress( $new_version ) {
 	global $wp_version, $pagenow, $action;
 
-	if ( version_compare( $wp_version, '3.3', '>=' ) )
+	if ( is_multisite() ) {
+		// Change to self_admin_url().
+		if ( version_compare( $wp_version, '3.4-alpha', '>=' ) )
+			return;
+	} elseif ( version_compare( $wp_version, '3.3', '>=' ) ) {
 		return;
+	}
 
 	// Ensure we only run this on the update-core.php page. wp_update_core() could be called in other contexts.
 	if ( 'update-core.php' != $pagenow )
@@ -624,12 +629,12 @@
 
 	// See do_core_upgrade()
 	show_message( __('WordPress updated successfully') );
-	show_message( '<span class="hide-if-no-js">' . sprintf( __( 'Welcome to WordPress %1$s. You will be redirected to the About WordPress screen. If not, click <a href="%s">here</a>.' ), $new_version, esc_url( admin_url( 'about.php?updated' ) ) ) . '</span>' );
-	show_message( '<span class="hide-if-js">' . sprintf( __( 'Welcome to WordPress %1$s. <a href="%2$s">Learn more</a>.' ), $new_version, esc_url( admin_url( 'about.php?updated' ) ) ) . '</span>' );
+	show_message( '<span class="hide-if-no-js">' . sprintf( __( 'Welcome to WordPress %1$s. You will be redirected to the About WordPress screen. If not, click <a href="%s">here</a>.' ), $new_version, esc_url( self_admin_url( 'about.php?updated' ) ) ) . '</span>' );
+	show_message( '<span class="hide-if-js">' . sprintf( __( 'Welcome to WordPress %1$s. <a href="%2$s">Learn more</a>.' ), $new_version, esc_url( self_admin_url( 'about.php?updated' ) ) ) . '</span>' );
 	echo '</div>';
 	?>
 <script type="text/javascript">
-window.location = '<?php echo admin_url( 'about.php?updated' ); ?>';
+window.location = '<?php echo self_admin_url( 'about.php?updated' ); ?>';
 </script>
 	<?php
 
Index: wp-admin/freedoms.php
===================================================================
--- wp-admin/freedoms.php	(revision 19687)
+++ wp-admin/freedoms.php	(working copy)
@@ -13,7 +13,7 @@
 
 list( $display_version ) = explode( '-', $wp_version );
 
-include( './admin-header.php' );
+include( ABSPATH . 'wp-admin/admin-header.php' );
 ?>
 <div class="wrap about-wrap">
 
@@ -54,4 +54,4 @@
 <p><?php _e( 'Don&#8217;t you wish all software came with these freedoms? So do we! For more information, check out the <a href="http://www.fsf.org/">Free Software Foundation</a>.' ); ?></p>
 
 </div>
-<?php include( './admin-footer.php' ); ?>
+<?php include( ABSPATH . 'wp-admin/admin-footer.php' ); ?>
Index: wp-admin/credits.php
===================================================================
--- wp-admin/credits.php	(revision 19687)
+++ wp-admin/credits.php	(working copy)
@@ -44,7 +44,7 @@
 
 list( $display_version ) = explode( '-', $wp_version );
 
-include( './admin-header.php' );
+include( ABSPATH . 'wp-admin/admin-header.php' );
 ?>
 <div class="wrap about-wrap">
 
@@ -73,7 +73,7 @@
 		'http://wordpress.org/about/',
 		/* translators: Url to the codex documentation on contributing to WordPress used on the credits page */
 		__( 'http://codex.wordpress.org/Contributing_to_WordPress' ) ) . '</p>';
-	include( './admin-footer.php' );
+	include( ABSPATH . 'wp-admin/admin-footer.php' );
 	exit;
 }
 
@@ -134,7 +134,7 @@
 </div>
 <?php
 
-include( './admin-footer.php' );
+include( ABSPATH . 'wp-admin/admin-footer.php' );
 
 return;
 
Index: wp-admin/update-core.php
===================================================================
--- wp-admin/update-core.php	(revision 19687)
+++ wp-admin/update-core.php	(working copy)
@@ -180,7 +180,7 @@
 		echo '<p>' . __( 'While your site is being updated, it will be in maintenance mode. As soon as your updates are complete, your site will return to normal.' ) . '</p>';
 	} else {
 		list( $normalized_version ) = explode( '-', $wp_version );
-		echo '<p>' . sprintf( __( '<a href="%s">Learn more about WordPress %s</a>.' ), esc_url( admin_url( 'about.php' ) ), $normalized_version ) . '</p>';
+		echo '<p>' . sprintf( __( '<a href="%s">Learn more about WordPress %s</a>.' ), esc_url( self_admin_url( 'about.php' ) ), $normalized_version ) . '</p>';
 	}
 	dismissed_updates();
 
@@ -382,12 +382,12 @@
 	}
 
 	show_message( __('WordPress updated successfully') );
-	show_message( '<span class="hide-if-no-js">' . sprintf( __( 'Welcome to WordPress %1$s. You will be redirected to the About WordPress screen. If not, click <a href="%s">here</a>.' ), $result, esc_url( admin_url( 'about.php?updated' ) ) ) . '</span>' );
-	show_message( '<span class="hide-if-js">' . sprintf( __( 'Welcome to WordPress %1$s. <a href="%2$s">Learn more</a>.' ), $result, esc_url( admin_url( 'about.php?updated' ) ) ) . '</span>' );
+	show_message( '<span class="hide-if-no-js">' . sprintf( __( 'Welcome to WordPress %1$s. You will be redirected to the About WordPress screen. If not, click <a href="%s">here</a>.' ), $result, esc_url( self_admin_url( 'about.php?updated' ) ) ) . '</span>' );
+	show_message( '<span class="hide-if-js">' . sprintf( __( 'Welcome to WordPress %1$s. <a href="%2$s">Learn more</a>.' ), $result, esc_url( self_admin_url( 'about.php?updated' ) ) ) . '</span>' );
 	?>
 	</div>
 	<script type="text/javascript">
-	window.location = '<?php echo admin_url( 'about.php?upgraded' ); ?>';
+	window.location = '<?php echo self_admin_url( 'about.php?upgraded' ); ?>';
 	</script>
 	<?php
 }
Index: wp-admin/about.php
===================================================================
--- wp-admin/about.php	(revision 19687)
+++ wp-admin/about.php	(working copy)
@@ -13,7 +13,7 @@
 
 list( $display_version ) = explode( '-', $wp_version );
 
-include( './admin-header.php' );
+include( ABSPATH . 'wp-admin/admin-header.php' );
 ?>
 <div class="wrap about-wrap">
 
@@ -38,8 +38,8 @@
 
 	<div class="feature-section images-stagger-right">
 		<div class="feature-images">
-			<img src="images/screenshots/media-icon.png" width="200" class="angled-right" />
-			<img src="images/screenshots/drag-and-drop.png" width="200" class="angled-left" />
+			<img src="<?php echo admin_url( 'images/screenshots/media-icon.png' ); ?>" width="200" class="angled-right" />
+			<img src="<?php echo admin_url( 'images/screenshots/drag-and-drop.png' ); ?>" width="200" class="angled-left" />
 		</div>
 		<div class="left-feature">
 			<h4><?php _e( 'File Type Detection' ); ?></h4>
@@ -69,12 +69,12 @@
 
 	<div class="feature-section screenshot-features">
 		<div class="angled-left">
-			<img src="images/screenshots/admin-flyouts.png" />
+			<img src="<?php echo admin_url( 'images/screenshots/admin-flyouts.png' ); ?>" />
 			<h4><?php _e( 'Responsive Design' ); ?></h4>
 			<p><?php _e( 'Certain dashboard screens have been updated to look better at various sizes, including improved iPad/tablet support.' ); ?></p>
 		</div>
 		<div class="angled-right">
-			<img src="images/screenshots/help-screen.png" />
+			<img src="<?php echo admin_url( 'images/screenshots/help-screen.png' ); ?>" />
 			<h4><?php _e( 'Help Tabs' ); ?></h4>
 			<p><?php _e( 'The Help tabs located in the upper corner of the dashboard screens below your name have gotten a facelift. Help content is broken into smaller sections for easier access, with links to relevant documentation and the support forums always visible.' ); ?></p>
 		</div>
@@ -86,8 +86,8 @@
 
 	<div class="feature-section images-stagger-right">
 		<div class="feature-images">
-			<img src="images/screenshots/new-feature-pointer.png" class="angled-right" />
-			<img src="images/screenshots/welcome-screen.png" class="angled-left" />
+			<img src="<?php echo admin_url( 'images/screenshots/new-feature-pointer.png' ); ?>" class="angled-right" />
+			<img src="<?php echo admin_url( 'images/screenshots/welcome-screen.png' ); ?>" class="angled-left" />
 		</div>
 		<div class="left-feature">
 			<h4><?php _e( 'New Feature Pointers' ); ?></h4>
@@ -109,7 +109,7 @@
 	<div class="feature-section three-col">
 		<div>
 			<h4><?php _e( 'Better Co-Editing' ); ?></h4>
-			<img src="images/screenshots/coediting.png" class="element-screenshot" />
+			<img src="<?php echo admin_url( 'images/screenshots/coediting.png' ); ?>" class="element-screenshot" />
 			<p><?php _e( 'Have you ever gone to edit a post after someone else has finished with it, only to get an alert that tells you the other person is still editing the post? From now on, you&#8217;ll only get that alert if another person is still on the editing screen &mdash; no more time lag.' ); ?></p>
 		</div>
 		<div>
@@ -161,17 +161,18 @@
 
 <div class="return-to-dashboard">
 	<?php if ( current_user_can( 'update_core' ) && isset( $_GET['updated'] ) ) : ?>
-	<a href="<?php echo esc_url( network_admin_url( 'update-core.php' ) ); ?>"><?php
+	<a href="<?php echo esc_url( self_admin_url( 'update-core.php' ) ); ?>"><?php
 		is_multisite() ? _e( 'Return to Updates' ) : _e( 'Return to Dashboard &rarr; Updates' );
 	?></a> |
 	<?php endif; ?>
-	<a href="<?php echo esc_url( admin_url() ); ?>"><?php _e( 'Go to Dashboard &rarr; Home' ); ?></a>
+	<a href="<?php echo esc_url( self_admin_url() ); ?>"><?php
+		is_network_admin() ? _e( 'Go to Dashboard' ) : _e( 'Go to Dashboard &rarr; Home' ); ?></a>
 </div>
 
 </div>
 <?php
 
-include( './admin-footer.php' );
+include( ABSPATH . 'wp-admin/admin-footer.php' );
 
 // These are strings we may use to describe maintenance/security releases, where we aim for no new strings.
 return;