I am using Linux Mint Cinnamon 14. I have set the $JAVA_HOME and $PATH environment variables in ~/.profile as follows:
update-java-alternatives
The java executable is not found with your JAVA_HOME, it only depends on your PATH.
update-java-alternatives is a good way to manage it for the entire system is through:
update-java-alternatives -l
Sample output:
java-7-oracle 1 /usr/lib/jvm/java-7-oracle
java-8-oracle 2 /usr/lib/jvm/java-8-oracle
Choose one of the alternatives:
sudo update-java-alternatives -s java-7-oracle
Like update-alternatives, it works through symlink management. The advantage is that is manages symlinks to all the Java utilities at once: javac, java, javap, etc.
I am yet to see a JAVA_HOME effect on the JDK. So far, I have only seen it used in third-party tools, e.g. Maven.