We've noticed the results page for Custom Google Search seems to break with some themes (seen the problem on a few Genesis themes so far). With the sidebar enabled on the results page, the results div takes the full width of the content area and the sidebar is pushed down below the bottom of the that div.
Managed to fix it by changing this line:
echo '<div id="content" role="main">';
echo '<div id="content" role="main" class="content">';
Looks like some themes aren't built with any elements that have an id of "content" so the styling doesn't work, doesn't get applied to the div created by the plugin. But these themes do have div's with a class called "content" -- so adding that class to the div generated by the plugin fixed the issue for us.