Installation checks for unicode et cetera, it could detect the MySQL strict mode too. Recent versions of MySQL have this on by default, and it prevents installation of Moodle anyway, so catching it before the nasty errors (see MDL-6218) would be a bonus. Maybe some short info text about how to disable the strict mode?

The SQL mode can be queried and checked, a bit like the character set, see http://dev.mysql.com/doc/refman/5.0/en/server-sql-mode.html.