Facebook was having a caching issue yesterday, which may have been the problem. If that's not it, you'll want to increase the width of the Like button in the Content plugin so that the faces show up to the right of the button or make sure that the Like button is not contained in a Div that has the following CSS property "overflow:hidden"
This would be in your Joomla template. You'll need to know what div is surrounding the article and Like button, and then check your template's CSS file for that div to see if there is the overflow:hidden setting set on it.