Is there a way to somehow verify that the googlebot finds the headings and the content, for example by word count?

I'm asking this because I tried a program called Screaming Frog, which fails to even fetch the first h1 on a validated page - for about 1/3 of all the pages(!) - and got insecure. Even though the site looks hunky dory in Webmaster Tools, I'd like to know what a googlebot-like content crawler finds on my page and in what order. Any tips on such tools is appreciated.

This is not about keyword count.