hatom errors

They’re markup errors from twentytwelve being an older theme. They’re not critical errors, merely structured data that Google wants to see.

You need to edit the theme – make a child theme Child Themes ? WordPress Codex – and include that markup. Use the Google Structured Data Testing Tool

Thank you for your suggestion – but suspect beyond my technical capabilities. What if I were to change theme?

Changing the theme will only work if the new theme has the correct structured data markup.

how do I know whether this is the case?

Best thing to do is ask the theme developers.