I've run into a situation where characters in a requested path that doesn't exist is causing a PDOException in the core statistics module. Here's the error:
PDOException: in statistics_exit() (line 93 of /path/public_html/modules/statistics/statistics.module).
This error is raised when attempting to add the "page not found" error to my database. I caught the exception and was able to tease out this error message:
SQLSTATE[HY000]: General error: 1366 Incorrect string value: '\xC2' for column 'path' at row 1
This is the full URL that includes the path that doesn't exist:
http://www.mysite.org/id-governor%C2
The "%C2" appears to be causing the error.