For me, on two different macs - a laptop and imac both running Mavericks 10.9.3 - the Java control panel would not allow for web access to be granted (submit would not stick, security level greyed out and couldn't be adjusted), and Safari couldn't load the java plugin.
Spent literally all day on this and the solutions here and on other threads would not fix the issues after multiple attempts to remove all/old java instances and re-install latest Java v7, Java v6, Java for OS X 2014-001 etc.
I tried Peter's suggestions and some of the follow-ups removing various java files by hand and restarting, re-installing, with no luck. Tired and ******-off I tossed everything I could find relating to java in the trash which then broke the OS's ability to complete the v7 installation - generating errors.
Defeated, I then did an OS reinstall via internet (command-R). Interestingly, a Safari security update - that was not available previously - magically appeared. Ran that. I then tested the java plugin in Safari on java.com and it was now working, showing that I had the latest version of java installed. Finally, I ran the java v7 installer again, which worked and gave me a working control panel in system preferences where I could enable web access settings.
Not a series of steps I would recommend or can explain but this is how I finally got java working on Mavericks. Figured I should post in case someone smarter than I can parse. Thanks for the ideas and fixes posted here.
And a rant to close. My wife is taking online courses running on Blackboard, which requires java. I hope there is a special place in **** for software developers that force down its users' throats Oracle's broken, insecure, bloated nightmare that is called java.