To give a few examples:
'content-type' header charset value should be 'utf-8'
'apple-touch-icon' link element was not specified.
I've asked myself if this might not even be due to the standard wordpress core setup? Can I improve the results without changing wordpress core to be more conform with the best practices?
For all those wo haven't heard of webhint yet: Webhints goal is to help web developers to write best possible code and clean up the web of bad practices. [from the FAQ]