I’m not sure about the feature image, I don’t have one on my site. And by plugging it into the facebook debugger, I mean just going to the debugger site and plug in the link for your blog post. That should force facebook to refresh anything it’s scraping your page for.
I was having this same exact problem. I found a plugin that populates the meta og:image property with the first image in your blogpost, which forces facebook to use that as the share image whether you are sharing from the like button or manually posting it on your profile. That, combined with putting the page through the facebook debugger, fixed the problem. The downside is that if I have multiple images in a post, I don’t have the option to choose a thumbnail – it forces you to take the first image. Maybe there’s a better plugin out there that allows you to choose from multiple images.
Here’s a link to the plugin: http://ww.wp.xz.cn/extend/plugins/facebook-like-thumbnail/ and make sure that you’re plugging your page into the facebook debugger too, to force it to re-scrape the page: http://developers.facebook.com/tools/debug