Theme Mentor is a cousin of the Theme-Check plugin getting deeper into the code analysis.
The higher the quality of your theme's code, the better the compatibility with the core and the plugins out there.
It's not required, but it's highly recommended. Theme Mentor is the extra step of notifying you for possible troubles with your code. Part of the remarks could be irrelevant, but hey, better to have something to double check and confirm it's working than to miss obvious code troubles.