Adobe has released updates for these versions (and earlier) of Flash Player: Flash Player 11.4.402.287 for Windows and Macintosh; Flash Player 126.96.36.199 for Linux; Flash Player 188.8.131.52 for Android 4.x; and Flash Player 184.108.40.206 for Android 3.x and 2.x. The updates are needed to fix a bug that attackers could exploit to crash Flash Player and possibly take over your system. See Adobe Security Bulletin 12-24 for more details.
The Microsoft Office for Mac 2008 12.3.4 update fixes a bug that causes a crash after you try the Insert Object command and then choose Display as Icon in the resulting dialog box. Mac users should be able to get the update from Microsoft Auto Update. Otherwise, you can look for it here.
Apple has released the Mac OS X 10.6 Update 10 for Java, with Java SE 6 upgrading to version 1.6.0_35.Given the number of recent malicious attacks coming via Java, this update configures web browsers to not automatically run Java applets that are found on the web. If you see one in your web browsing, you will see an "Inactive plug-in" message. Click that, and the applet will run. ZD Net has more about the security issue here.
The new Gmail 1.3.1 app for the iPad has a number of unspecified bug fixes. It also says you will have the option to open links in email with the Chrome browser if installed. (Google says "Take that, Safari!") The update should be in the App Store.
According to Google, here is the current list of software that has compatibility problems with the Google Chrome browser (not really a list of big-name apps): Safe Eyes Parental Control Software, ContentWatch, Microsoft Office XP Input Method, Editor, Naomi Web Filter, Trusteer Rapport, Hide My IP, Venturi Firewall, and PPLive. There are some more problems, with workarounds. listed here.
The SANS Internet Storm Center has multiple reports of a phishing attack that looks very much like a legitimate Microsoft email regarding Important Changes to Microsoft Services Agreement and Communication Preferences. If you receive an email like this, do not click on any links until you can determine whether this is a legit email or not. SANS has more details on the attack, and they way to check emails, here.
According to ComputerWorld, a bug in Java 7, which is included in the 1.7 JRE (Java Runtime Environment), makes Windows, Linux, and Mac OS X machines vulnerable. Details on what is described as a "super-dangerous" bug can be found here. The best defense may be to disable Java until it is patched.
Apple has a number of bug fixes in iTunes 10.6.3. The new version fixes a bug that may lock up iTunes when syncing to a 1st generation iPad that has iBooks textbooks on it. It also fixes bugs that may delete playlists, delete apps, or scramble the order of photos. Find out more here, and then download it via Software Update.
Apple probably wouldn't say this in their release notes, since it would be admitting there was a problem in the first place, but reports are that the OS X 10.8.1 Mountain Lion Update takes care of battery life problems in Macbooks that some users were reporting with the 10.8 version. Ars Technica has more details.