Software UpdateからSafari 5.1.4がダウンロードできるようになっています。5.1.4の主な改良点は以下の通り。ダウンロードしたSafari 5.1.4のファイルサイズは46.4MBありました。

1. Improve JavaScript performance
2. Improve responsiveness when typing into the search field after changing network configurations or with an intermittent network connection
3. Address an issue that could cause webpages to flash white when switching between Safari windows
4. Address issues that prevented printing U.S. Postal Service shipping labels and embedded PDFs
5. Preserve links in PDFs saved from webpages
6. Fix an issue that could make Flash content appear incomplete after using gesture zooming
7. Fix an issue that could cause the screen to dim while watching HTML5 video
8. Improve stability, compatibility and startup time when using extensions
9. Allow cookies set during regular browsing to be available after using Private Browsing
10. Fix an issue that could cause some data to be left behind after pressing the “Remove All Website Data” button

上記改良点の中で私がSafari 5.1.3で不具合を確認していたのは#7の「HTML5動画閲覧時に画面が暗くなる問題」ですが、このアップデートで修正されたようです。