Fixing Structured Data Errors on Google Webmaster Tools
The most common errors found on the structured data tool in WMT are entity-title, author, and date updated. Most themes these days seem to be getting the entity-title right, but some older themes are missing the required code.
Getting This Wrong Will Likely Break Your Site
If you are not comfortable editing your website's code, DON'T. If you aren't comfortable editing code, take the example bits of code that follow and pay someone to do it for you, or send your theme author a donation and ask him or her to make the required changes.
If you are still reading this tutorial and are determined to make these fixes yourself, make a copy of all your theme files right now on your computer using FTP with filezilla or whatever file management program you use. Keep these files handy in case you break your site.
Turn off any file caching like WP Super Cache so changes are reflected in your site.
Every WordPress theme is different. Sometimes fixing a problem in one place fixes the whole site. More complex themes have multiple files which produce the same output but each file has subtle differences... all of which need to be fixed. Most themes treat the blog page and a single page of content differently - meaning any change you make to fix a structured error issue on the blog page won't fix the same error on the single content page.