Any messages you are seeing with the debug output should be resolved. These often point to holes in the current logic within your theme.
If your goal is to submit the theme to the WordPress Theme Directory you have to resolve any PHP errors, warnings, or notices for the theme to be approved.
Themes must not generate any Theme-Check Warning or Required notices. Themes must not generate any WordPress deprecated-function or _doing_it_wrong() notices, PHP errors, warnings, or notices, HTML/CSS validation errors, or JavaScript errors.