According to the Servlet spec, you need to put the filter init-param inside the filter tag rather than the filter-mapping tag.
Code:
<filter>
<filter-name>OpenSessionInViewFilter</filter-name>
<filter-class>org.springframework.orm.hibernate.support.OpenSessionInViewFilter</filter-class>
<init-param>
<param-name>sessionFactoryBeanName</param-name>
<param-value>mySessionFactory</param-value>
</init-param>
</filter>
<filter-mapping>
<filter-name>OpenSessionInViewFilter</filter-name>
<url-pattern>*.do</url-pattern>
</filter-mapping>
Juergen