See, Facebook does more than simply let you send things to their pages and so forth. More and more, they’re becoming a search engine. Facebook actually crawls the web, to some degree.
When you click a Facebook Like button, Facebook’s servers retrieve the webpage you’re viewing, and parse it for the OpenGraph meta tags. These tags tell Facebook what content to display for a link. The title, the image, maybe audio or video, etc. SFC does a pretty good job of automatically populating your entire website with these OpenGraph tags, invisibly (side note, Google+ will use these same tags, although they also have their own set of tags you can use too).
Generally, users who email me about this problem are just using SFC for the first time, and have previously had Like buttons on their page manually, or have been sharing their links on Facebook manually at some other point. This is where they run into the issue: Facebook caches the results of this crawl, usually for a long time. So when somebody clicks a Like button, it doesn’t have to pull the contents of the page if it’s already pulled those contents once before. So since SFC is now populating the OpenGraph meta tags, but FB is reading the cached version instead, the data doesn’t match up.
There’s a simple one-time fix for this problem. Facebook has made an OpenGraph debugger tool:
On this page, you’ll find a simple box asking for a URL. Put in the URL of the page having the problem, and the tool will go and force retrieve the content of the page and display the parsed OpenGraph meta tags.
Now, this is meant to be a debugging tool for people trying to add OpenGraph tags to their site, but it has a rather nice side-effect. When it forcibly retrieves the page, it also updates Facebook’s cached info for that URL. So all you have to do to make Facebook see your updated content is to take the problem URL, put it in there, and hit the Debug button. Now go back to the page, refresh it, and try the Like/Send button again. Voila, it’s magically fixed to show whatever the Debugger tool saw.
So if you’re having trouble getting some particular page to work in the way you’re expecting, try the debugger tool on the URL first.