Microsoft AntiSpyware keeps a few logs about the user and other information containing scan history and errors found.
Besides information logged for the user and available though the application it self, there are two ASCII text logs in \program files\Microsoft AntiSpyware:
cleaner.log shows the actions taken in cleaning runs
errors.log collects (sometimes vast numbers of) error/debug messages.
They occasionally grow in file size and become uncontrolled.