I had a similar issue. Make sure you have all other programs closed at the time of the install, especially Office apps (like Word, Outlook, Excel, etc.). Outlook was causing my issue. Once I close it, the install worked fine.
I have tried installing in safe mode - no help, in safe mode I get an error that AcroRead.msi cannot be trusted due to software restriction policy processing.
I then tried in normal boot, but with startup items disabled via msconfig. This also aborts like before with the error when temporary files are being removed stating Setup was interrupted before Adobe Reader could be completely installed.
I looked at the Adobe log file and the last item in it says it ended with code 0 - there are no errors indicated in the log file.
The error in the application event log is error code 1603 with event 1024, suggesting that logging be enabled for the Windows Installer - I tried that, but no MSI.log was created and I suspect that the Windows Installer is not being used by Adobe 10 installation.
At this point, I am at a loss as to what is going wrong or where to look. I have installed Foxit reader to allow our work to proceed in the interim but am interested in finding the cause of the problem since it may also effect other things.
See this article for more information on the 1603 error: http://support.microsoft.com/kb/834484
Are you installing as an Administrator user?
Does the event log give you any information what folder is causing the error?