.jar files association does not work if 32 and 64 bit JREs were installed and then one of the JREs was uninstalled. JRE uninstall does not recover jarfile reg entry on 64bit systems.
Reg keys verification was added and 32v64Matrix tests show the following:
Install JRE 7u5 b05 32 bit + JRE 7u5 b05 64 bit, remove JRE 7u5 b05 32 bit
Keys not found:
HKEY_CLASSES_ROOT\.jar
HKEY_LOCAL_MACHINE\Software\Classes\.jar
HKEY_LOCAL_MACHINE\Software\Classes\jarfile
HKEY_LOCAL_MACHINE\Software\Classes\JNLPFile

HKEY_CLASSES_ROOT\JNLPFile
 Expected => (Default) REG_SZ JNLP File EditFlags REG_BINARY 00000100
 Actual =>
HKEY_CLASSES_ROOT\Applications\java.exe
 Expected => IsHostApp REG_SZ
 Actual =>
HKEY_LOCAL_MACHINE\Software\Classes\Applications\java.exe
 Expected => IsHostApp REG_SZ
 Actual =>
HKEY_CLASSES_ROOT\Applications\javaw.exe
 Expected => IsHostApp REG_SZ
 Actual =>
HKEY_LOCAL_MACHINE\Software\Classes\Applications\javaw.exe
 Expected => IsHostApp REG_SZ
 Actual =>

Strange values:
HKEY_CLASSES_ROOT\jarfile
 Looked for => Executable Jar File
 String searched .7.0_05"