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Sorry, people. I should have added the disclaimer, "...your mileage may vary"

To confirm what others have reported —

advcheck.dll was renamed advcheck.dll_old before installing advcheck162.exe.

I then scanned for problems with Firefox 3.0.12 open, and upon completion...

I run WinXP SP3 as an Admin account, use Firefox 3.0.12, and get the error messages regardless of whether FF is open or closed throughout the complete scan, or closed while the scan is in progress.
...

FWIW, I ran Spybot S&D from a system account (i.e., in a WinXP Command Prompt from C:\WINDOWS\system32\>...) and I was unable to reproduce any of the earlier errors.

I'll leave it to you...