I just installed jre-7u9-macosx-x64.dmg on OSX 10.8.2 and using Safari 6.0.2 and I can now access mydlink.com and my DIR-865L cloud router. I noticed that before installing 7, I tried to install Java 6 and it installed however the Java Preferences did not appear in the Utilities folder and was not listed in System Preferences. So I installed Java 7 and I can now access the router on mydlink.com and Java is an icon in System Preferences. Not sure if this helps anyone with a DCS camera or not. I would phone contact DLink support, level 2 or higher and talk to someone and let them now about this issue with Java and OSX 10.8. The more visibility they see that users are having a problem with this, the more it will get reviewed and fixed sooner. I've found that using email with DLink is less than desired in moving problems thru DLink. Call and get help.
Keep us posted.