Index: src/wp-admin/includes/update.php
===================================================================
--- src/wp-admin/includes/update.php	(revision 26053)
+++ src/wp-admin/includes/update.php	(working copy)
@@ -364,8 +364,15 @@
 		 * This flag is cleared whenever a successful update occurs using Core_Upgrader.
 		 */
 		$comparison = ! empty( $failed['critical'] ) ? '>=' : '>';
-		if ( version_compare( $failed['attempted'], $wp_version, '>=' ) )
-			$nag = true;
+		if ( version_compare( $failed['attempted'], $wp_version, $comparison ) ) {
+			require_once ABSPATH . 'wp-admin/includes/class-wp-upgrader.php';
+			$upgrader = new Core_Upgrader;
+
+			if ( $upgrader->check_files() )
+				delete_site_option( 'auto_core_update_failed' );
+			else
+				$nag = true;
+		}
 	}
 
 	if ( ! $nag )