Microsoft Knowledge Base Article 902093 contains the following summary and introduction:

SUMMARY

By default, the Windows Update client records all transaction information to the following log file:

%windir%\Windowsupdate.log

If you receive an error message on the Microsoft Windows Update Web site or from the Automatic Updates service, you can use the information that is included in the Windowsupdate.log log file to troubleshoot the issue.

INTRODUCTION

This article describes how to read the Windowsupdate.log file. To view the log file, follow these steps:

1. Click Start, and then click Run.

2. In the Open box, type %windir%\windowsupdate.log, and then click OK.