Index: src/wp-admin/css/dashboard.css
===================================================================
--- src/wp-admin/css/dashboard.css	(revision 34906)
+++ src/wp-admin/css/dashboard.css	(working copy)
@@ -115,7 +115,7 @@
 	line-height: 2.1em;
 }
 
-.welcome-panel h3 {
+.welcome-panel h2 {
 	margin: 0;
 	font-size: 21px;
 	font-weight: normal;
@@ -122,7 +122,7 @@
 	line-height: 1.2;
 }
 
-.welcome-panel h4 {
+.welcome-panel h3 {
 	margin: 1.33em 0 0;
 	font-size: 16px;
 }
@@ -360,8 +360,11 @@
 	overflow: hidden;
 }
 
-#dashboard-widgets h4.mu-storage {
-	margin-bottom: 10px;
+#dashboard-widgets h3.mu-storage {
+	margin: 0 0 10px;
+	padding: 0;
+	font-size: 14px;
+	font-weight: normal;
 }
 
 /* Dashboard right now - Colors */
@@ -378,7 +381,7 @@
 	padding: 10px 12px 6px 12px;
 }
 
-#dashboard_right_now .sub h4 {
+#dashboard_right_now .sub h3 {
 	color: #555;
 }
 
@@ -537,11 +540,6 @@
 	border: none;
 }
 
-#dashboard_quick_press .drafts h4 {
-	margin: 0 12px 8px;
-	font-weight: normal;
-}
-
 #dashboard_quick_press .drafts .view-all {
 	float: right;
 	margin: 0 12px 0 0;
@@ -576,21 +574,19 @@
 	margin: 0 5px 0 0;
 }
 
-/* Dashboard activity widget */
+/* Dashboard common styles */
 
-#dashboard-widgets #dashboard_activity h4 {
-	margin: 0 0 8px 12px;
+#dashboard-widgets #dashboard_activity h3,
+#dashboard_quick_press .drafts h2 {
+	margin: 0 12px 8px;
+	padding: 0;
+	font-size: 14px;
 	font-weight: normal;
+	color: #23282d;
 }
 
-#dashboard-widgets #dashboard_activity h4.comment-meta {
-	margin: 0;
-}
+/* Dashboard activity widget */
 
-#dashboard_activity h4.comment-meta {
-	margin-bottom: 4px;
-}
-
 #dashboard_activity ul {
 	padding: 0 12px;
 }
@@ -708,11 +704,6 @@
 	margin: 1em 0;
 }
 
-#activity-widget #the-comment-list .comment-item h4 {
-	font-size: 13px;
-	color: #999;
-}
-
 #activity-widget #the-comment-list .comment-item p.row-actions {
 	margin: 4px 0 0 0;
 }
@@ -794,14 +785,6 @@
 	right: 33px;
 }
 
-#dashboard-widgets h4 {
-	color: #23282d;
-	font-weight: normal;
-	font-size: 14px;
-	margin: 0 0 .2em;
-	padding: 0;
-}
-
 #dashboard_plugins h5 {
 	font-size: 14px;
 }
@@ -834,13 +817,13 @@
 	border-top: none;
 }
 
-#latest-comments #the-comment-list .comment-item h4 {
+#latest-comments #the-comment-list .comment-meta {
 	line-height: 1.5em;
-	margin-top: 0;
+	margin: 0;
 	color: #666;
 }
 
-#latest-comments #the-comment-list .comment-item h4 cite {
+#latest-comments #the-comment-list .comment-meta cite {
 	font-style: normal;
 	font-weight: normal;
 }
Index: src/wp-admin/includes/dashboard.php
===================================================================
--- src/wp-admin/includes/dashboard.php	(revision 34906)
+++ src/wp-admin/includes/dashboard.php	(working copy)
@@ -530,9 +530,9 @@
 
 	echo '<div class="drafts">';
 	if ( count( $drafts ) > 3 ) {
-		echo '<p class="view-all"><a href="' . esc_url( admin_url( 'edit.php?post_status=draft' ) ) . '">' . _x( 'View all', 'drafts' ) . "</a></p>\n";
+		echo '<p class="view-all"><a href="' . esc_url( admin_url( 'edit.php?post_status=draft' ) ) . '" aria-label="' . __( 'View all drafts' ) . '">' . _x( 'View all', 'drafts' ) . "</a></p>\n";
  	}
-	echo '<h4 class="hide-if-no-js">' . __( 'Drafts' ) . "</h4>\n<ul>";
+	echo '<h2 class="hide-if-no-js">' . __( 'Drafts' ) . "</h2>\n<ul>";
 
 	$drafts = array_slice( $drafts, 0, 3 );
 	foreach ( $drafts as $draft ) {
@@ -638,7 +638,7 @@
 			<?php if ( !$comment->comment_type || 'comment' == $comment->comment_type ) : ?>
 
 			<div class="dashboard-comment-wrap has-row-actions">
-			<h4 class="comment-meta">
+			<p class="comment-meta">
 				<?php
 				if ( $comment_post_link ) {
 					printf(
@@ -657,7 +657,7 @@
 					);
 				}
 				?>
-			</h4>
+			</p>
 
 			<?php
 			else :
@@ -675,7 +675,7 @@
 			?>
 			<div class="dashboard-comment-wrap has-row-actions">
 			<?php /* translators: %1$s is type of comment, %2$s is link to the post */ ?>
-			<h4 class="comment-meta"><?php printf( _x( '%1$s on %2$s', 'dashboard' ), "<strong>$type</strong>", $comment_post_link ); ?></h4>
+			<p class="comment-meta"><?php printf( _x( '%1$s on %2$s', 'dashboard' ), "<strong>$type</strong>", $comment_post_link ); ?></p>
 			<p class="comment-author"><?php comment_author_link( $comment ); ?></p>
 
 			<?php endif; // comment_type ?>
@@ -765,7 +765,7 @@
 
 		echo '<div id="' . $args['id'] . '" class="activity-block">';
 
-		echo '<h4>' . $args['title'] . '</h4>';
+		echo '<h3>' . $args['title'] . '</h3>';
 
 		echo '<ul>';
 
@@ -841,7 +841,7 @@
 
 	if ( $comments ) {
 		echo '<div id="latest-comments" class="activity-block">';
-		echo '<h4>' . __( 'Comments' ) . '</h4>';
+		echo '<h3>' . __( 'Comments' ) . '</h3>';
 
 		echo '<div id="the-comment-list" data-wp-lists="list:comment">';
 		foreach ( $comments as $comment )
@@ -1211,7 +1211,7 @@
 	$percentused = number_format( $percentused );
 
 	?>
-	<h4 class="mu-storage"><?php _e( 'Storage Space' ); ?></h4>
+	<h3 class="mu-storage"><?php _e( 'Storage Space' ); ?></h3>
 	<div class="mu-storage">
 	<ul>
 		<li class="storage-count">
@@ -1365,12 +1365,12 @@
 function wp_welcome_panel() {
 	?>
 	<div class="welcome-panel-content">
-	<h3><?php _e( 'Welcome to WordPress!' ); ?></h3>
+	<h2><?php _e( 'Welcome to WordPress!' ); ?></h2>
 	<p class="about-description"><?php _e( 'We&#8217;ve assembled some links to get you started:' ); ?></p>
 	<div class="welcome-panel-column-container">
 	<div class="welcome-panel-column">
 		<?php if ( current_user_can( 'customize' ) ): ?>
-			<h4><?php _e( 'Get Started' ); ?></h4>
+			<h3><?php _e( 'Get Started' ); ?></h3>
 			<a class="button button-primary button-hero load-customize hide-if-no-customize" href="<?php echo wp_customize_url(); ?>"><?php _e( 'Customize Your Site' ); ?></a>
 		<?php endif; ?>
 		<a class="button button-primary button-hero hide-if-customize" href="<?php echo admin_url( 'themes.php' ); ?>"><?php _e( 'Customize Your Site' ); ?></a>
@@ -1379,7 +1379,7 @@
 		<?php endif; ?>
 	</div>
 	<div class="welcome-panel-column">
-		<h4><?php _e( 'Next Steps' ); ?></h4>
+		<h3><?php _e( 'Next Steps' ); ?></h3>
 		<ul>
 		<?php if ( 'page' == get_option( 'show_on_front' ) && ! get_option( 'page_for_posts' ) ) : ?>
 			<li><?php printf( '<a href="%s" class="welcome-icon welcome-edit-page">' . __( 'Edit your front page' ) . '</a>', get_edit_post_link( get_option( 'page_on_front' ) ) ); ?></li>
@@ -1396,7 +1396,7 @@
 		</ul>
 	</div>
 	<div class="welcome-panel-column welcome-panel-last">
-		<h4><?php _e( 'More Actions' ); ?></h4>
+		<h3><?php _e( 'More Actions' ); ?></h3>
 		<ul>
 		<?php if ( current_theme_supports( 'widgets' ) || current_theme_supports( 'menus' ) ) : ?>
 			<li><div class="welcome-icon welcome-widgets-menus"><?php