Show HTML errors in Google Chrome?

I'm not sure it can do exactly what you're after without an extension. You can use the developer tools to explore the HTML to see if it is what you expect/intend, but I don't think it will tell you where there are errors.

HTML browsers are designed to be able to taken invalid markup and render it as best they can. It will have a very high tolerance for errors.

You may want to try an extension like one of these.

Another options is to use the W3C validator "favelets" to open the W3C validator from a bookmark.

http://validator.w3.org/favelets.html

~Use HTML Validator extension.~

https://chrome.google.com/webstore/detail/html-validator/mpbelhhnfhfjnaehkcnnaknldmnocglk.