FULL PRODUCT VERSION :
java version "1.6.0_13"
Java(TM) SE Runtime Environment (build 1.6.0_13-b03)
Java HotSpot(TM) Client VM (build 11.3-b02, mixed mode, sharing)

ADDITIONAL OS VERSION INFORMATION :
Microsoft Windows XP [Version 5.1.2600]

EXTRA RELEVANT SYSTEM CONFIGURATION :
Both jre5 and jre6 are installed.

A DESCRIPTION OF THE PROBLEM :
The java "Configuration completed successfully" step of the installer is removing all copies of java.exe, javaw.exe, and javaws.exe from system32. This means that java cannot be started from the path.
The jre6 install is failing the first time. I assume this is due open file locking while the java is running (win32) and the update inplace deployment at odds with each other.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
1. The offline installer is being run by the network admin on the local network.
2. JRE5 is being updated first without problems.
3. JRE6 is failing to update (I assume due to open file locking on win32).
4. Reinstall JREs.
5. Configuration completed, removes the files.

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
C:\WINDOWS\system32>dir java*.exe
144,792 java.exe
144,792 javaw.exe
148,888 javaws.exe
               3 File(s) 438,472 bytes
ACTUAL -
C:\WINDOWS\system32>dir java*.exe
File Not Found


ERROR MESSAGES/STACK TRACES THAT OCCUR :
'java' is not recognized as an internal or external command,
operable program or batch file.

'javaw' is not recognized as an internal or external command,
operable program or batch file.

'javaws' is not recognized as an internal or external command,
operable program or batch file.

REPRODUCIBILITY :
This bug can be reproduced often.

---------- BEGIN SOURCE ----------
  From EventLog (oldest event is at the top newest event at bottom):

Product: J2SE Runtime Environment 5.0 Update 17 -- Removal completed successfully.
Product: J2SE Runtime Environment 5.0 Update 18 -- Installation operation completed successfully.
Product: Java(TM) 6 Update 11 -- Error 1722.There is a problem with this Windows Installer package. A program run as part of the setup did not finish as expected. Contact your support personnel or package vendor. Action FilesInUseDialog, location: C:\WINDOWS\Installer\MSI26.tmp, command: C:\Program Files\Java\jre6Product: Java(TM) 6 Update 13 -- Installation operation failed.
Product: J2SE Runtime Environment 5.0 Update 18 -- You already have this version of the JRE installed. Please uninstall the product through your add/remove programs utility before reinstalling.
Product: J2SE Runtime Environment 5.0 Update 18 -- Configuration failed.
Product: Java(TM) 6 Update 13 -- Installation operation completed successfully.
Product: Java(TM) 6 Update 13 -- Configuration completed successfully.
---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
1. Copy the java*.exe files from jre6/bin to system32.
2. Keep reinstalling the jre until it works.