10/26/2012 Update: Apple has posted a step-by-step walkthrough on how to roll back to Java SE 6 - you can find that post here.
The new Java update (Java for OS X 2012-006) can leave you without operable Java on Mac, which will mean you will not be able to use the Local File Linking feature in Shotgun. Tank also depends on Java for its browser integration features.
OSX "Software Update" System dialog
Apple Java Update (from App Store)
Here is the Apple support post describing this update:
From the article: "This update uninstalls the Apple-provided Java applet plug-in from all web browsers. To use applets on a web page, click on the region labeled "Missing plug-in" to go download the latest version of the Java applet plug-in from Oracle."
Shotgun's Java functionality is behind-the-scenes, so you will unfortunately not see a "Missing plug-in" message or link to download. That download link would send you here:
...but unfortunately that won't help you much. From the article: "Chrome does not support Java 7. Java 7 runs only on 64-bit browsers and Chrome is a 32-bit browser. If you download Java 7, you will not be able to run Java content in Chrome and will need to use a 64-bit browser (such as Safari or Firefox) to run Java content within a browser. Additionally, installing Java 7 will disable the ability to use Apple Java 6 on your system."
In initial testing, we've found that Java 7 does not play well with Shotgun's Local File Linking in Firefox or Safari, and as Java article mentions, is not supported on Chrome at all.
If you have installed this update, you will experience errors or browser lockups when trying to use the "Link to Local Files" button in Shotgun, and may have issues with the browser integration in Tank as well. We are working on a process for restoring your Java environment to a state that will work with Shotgun in all browsers. We will post that as soon as we have it documented and confirmed. [Update: fix posted at the top of this article]