Maybe you have already noticed that starting from Mac OS X 10.8 (Mountain Lion), Apple had changed the popup displayed when you try to open a web page with a Java applet.
Now it looks like this:
A signed applet comes with a signature which should be verified by a browser, which checks if the code signing certificate is valid and issued by a trusted source. As soon as the signature is verified, an applet is launched in the browser. Technically, signed applets can get more control over a client computer, like access to the file system, registry and so on. The Java standard admits that a web browser should show a popup window in order to get approval from a user. On PCs this popup window is modest and just informs a user that an applet that is signed with a verified certificate is about to launch.
Apple decided to go a different way. Apple displays the popup windows which you see in this post. It says that "the digital signature could not be verified" even if it is signed with the correct certificate. Of course, end-users, who are not computer-savvy, are confused with this dialog and click the "Deny" button, which prevents the launching of the applet. They then cannot use important services (e.g. banking software) that they go to websites for, or try to contact a company's technical support.Companies cannot do anything because the problem with the applet's confusing message is out of their control. All they can do is to instruct users to click the "Allow" button. It sounds very simple but the problem is pretty serious because there are so many confused users who, ironically, are preventing themselves from getting services. If you Google this problem, you will find that a lot of companies all over the world are running afoul of this issue.
Apple support keeps saying that the verification logic has been changed in Mac OS X 10.8. "Unidentified developer" means a source other than the Mac App Store or a Developer ID-identified developer. Taking into account that Java applets cannot participate in the Mac OS Developer program, there is no way to address this issue on Apple platforms. This is really sad news...