Chrome 35 unprefixes the new Shadow DOM implementation (blog post) and turns it on by default. Some of what you're seeing could also be differences between native Shadow DOM and the polyfill shimming.
Without having the codebase to look at, there could be any number of things. There have been many updates to Shadow DOM's styling features in the last few months.
Things to note from what I saw on your site
@host { :scope {display: block;} }
->:host {display: block; }
- move stylesheets an element relies on into the
<polymer-element>
. applyAuthorStyles
is gone. If you were using it, the only way to take on styles from the outer page is to use::shadow
,/deep/
, or include shared styles in the<polymer-element>
the needs it.- If you're using
<content>
and distributed nodes, make sure you're using the::content
pseudo element
Here are some up to date resources for styling: