Relevant WindowsUpdate.log entries:
C:\WINDOWS\TEMP\InstallAX_12_0_0_77.exe is created during the update installation process, but vanishes when the update fails so I don't believe it's a permissions issue.
2014-03-25 10:25:50:253 1172 4bc Agent *************
2014-03-25 10:25:50:253 1172 4bc Agent ** START ** Agent: Installing updates [CallerId = AutomaticUpdatesWuApp]
2014-03-25 10:25:50:253 1172 4bc Agent *********
2014-03-25 10:25:50:253 1172 4bc Agent * Updates to install = 1
2014-03-25 10:25:50:257 1172 4bc Agent * Title = Adobe Flash Player 32-bit/64-bit ActiveX 12.0.0.77
2014-03-25 10:25:50:257 1172 4bc Agent * UpdateId = {7FD7DFEF-C83F-4B17-914F-F2CC362C194B}.1
2014-03-25 10:25:50:299 1172 4bc DnldMgr Preparing update for install, updateId = {7FD7DFEF-C83F-4B17-914F-F2CC362C194B}.1.
2014-03-25 10:25:50:300 9128 117c Misc =========== Logging initialized (build: 7.9.9600.16422, tz: +1100) ===========
2014-03-25 10:25:50:300 9128 117c Misc = Process: C:\WINDOWS\system32\wuauclt.exe
2014-03-25 10:25:50:300 9128 117c Misc = Module: C:\WINDOWS\SYSTEM32\wuaueng.dll
2014-03-25 10:25:50:300 9128 117c Handler :::::::::::::
2014-03-25 10:25:50:300 9128 117c Handler :: START :: Handler: MSI Install
2014-03-25 10:25:50:300 9128 117c Handler :::::::::
2014-03-25 10:25:50:300 9128 117c Handler : Updates to install = 1
2014-03-25 10:25:50:302 9128 117c Handler MSI update {7FD7DFEF-C83F-4B17-914F-F2CC362C194B}.1 using source image from 1 CABs.
2014-03-25 10:25:50:536 9128 117c Handler : Batch installing 1 updates
2014-03-25 10:25:50:537 9128 117c Handler List of MSPs in transaction:
2014-03-25 10:25:50:537 9128 117c Handler List of Transforms in transaction:
2014-03-25 10:25:50:537 9128 117c Handler MSI final command line: ALLUSERS=1 MSIRESTARTMANAGERCONTROL=Disable REBOOT=REALLYSUPPRESS
2014-03-25 10:25:54:147 1172 3c4 Report REPORT EVENT: {ADD81270-D52B-463C-8F0F-ABF3482E2256} 2014-03-25 10:25:49:147+1100 1 162 [AGENT_DOWNLOAD_SUCCEEDED] 101 {7FD7DFEF-C83F-4B17-914F-F2CC362C194B} 1 0 AutomaticUpdatesWuApp Success Content Download Download succeeded.
2014-03-25 10:25:54:147 1172 3c4 Report REPORT EVENT: {B1E9935E-C9F5-47A6-8870-8F838991034F} 2014-03-25 10:25:49:147+1100 1 189 [AU_UNSCHEDULED_INSTALL_READY] 102 {00000000-0000-0000-0000-000000000000} 0 0 AutomaticUpdates Success Content Install Installation Ready: The following updates are downloaded and ready for installation. To install the updates, an administrator should log on to this computer and Windows will prompt with further instructions: - Adobe Shockwave Player 12.0 - Google Chrome 33.0.1750.154 - Microsoft Visual Studio 2010 Service Pack 1 - Adobe Flash Player 32-bit/64-bit ActiveX 12.0.0.77
2014-03-25 10:25:54:147 1172 3c4 Report CWERReporter finishing event handling. (00000000)
2014-03-25 10:26:11:242 9128 117c Handler MSP Error List:
2014-03-25 10:26:11:242 9128 117c Handler 1: 1722 2: NewCustomAction1 3: C:\WINDOWS\TEMP\InstallAX_12_0_0_77.exe 4: -install -msi
2014-03-25 10:26:11:242 9128 117c Handler : MSI transaction completed. MSI: 0x80070643, Handler: 0x8024200b, Source: No, Reboot: 0
2014-03-25 10:26:11:242 9128 117c Handler Updating status for update 0.
2014-03-25 10:26:11:242 9128 117c Handler : WARNING: First failure for update {7FD7DFEF-C83F-4B17-914F-F2CC362C194B}, transaction error = 0x8024200b, MSI result = 0x80070643, MSI action = NewCustomAction1
2014-03-25 10:26:11:243 9128 117c Handler Sending completion notification for update 0 ({7FD7DFEF-C83F-4B17-914F-F2CC362C194B}.1).
2014-03-25 10:26:11:243 9128 117c Handler Stopping on first error due to FailOptTerminate.
2014-03-25 10:26:11:243 9128 117c Handler : WARNING: Operation failed at update 0, Exit code = 0x8024200B
2014-03-25 10:26:11:243 9128 117c Handler :::::::::
2014-03-25 10:26:11:243 1172 16b4 AU >>## RESUMED ## AU: Installing update [UpdateId = {7FD7DFEF-C83F-4B17-914F-F2CC362C194B}]
2014-03-25 10:26:11:243 9128 117c Handler :: END :: Handler: MSI Install
2014-03-25 10:26:11:243 1172 16b4 AU # WARNING: Install failed, error = 0x80070643 / 0x000006BA
2014-03-25 10:26:11:243 9128 117c Handler :::::::::::::
2014-03-25 10:26:11:252 1172 4bc Agent *********
2014-03-25 10:26:11:252 1172 4bc Agent ** END ** Agent: Installing updates [CallerId = AutomaticUpdatesWuApp]
2014-03-25 10:26:11:252 1172 4bc Agent *************
EditC:\WINDOWS\TEMP\InstallAX_12_0_0_77.exe is created during the update installation process, but vanishes when the update fails so I don't believe it's a permissions issue.