Yup, there's 2 issues here:
Like link on the home page:
The post from above describes this the best:
www.sourcecoast.com/forums/topic?id=1392&p=1#p5539
Basically, the Like button, when you're not using the url parameter in the tag, will always display the link for the 'current' page. If it's being shown on the home/front page, that's your link. If it's in a category view, that's your link. Etc. We are working on a content plugin for some of the widgets, and this realization of the problems with url generation is just making the release of the content plugin a higher priority.
Current Fix(es): 1) Use the url= parameter in your articles so that wherever they are displayed, the link will always be correct.
2) Use intro text and full text in your article, and use the non-url version of the JFBCLike tag. Since the intro text won't display the Like, you won't have the wrong URL. Since the full text will (on the article view only), the link will be to the correct page. You can either put the like button at the bottom of the article, or if you set "Show Intro Text" to no on the article, you can keep it at the top (but will have to duplicate the intro text into the fulltext) -- lemme know if that's confusing, and I can explain more.
When editing on the front-end, the link is wonky:
Yep, you found another bug we hadn't reasoned through. We prevent the plugin from running when you're in the admin area, so that even when you're editing an article the {} tag shows (not what we replace it with... <fb:like ... Since you're editing on the front end, what's happening is that when you open the article to edit, our plugin is replacing our tag (in the html text box) with the Facebook like markup. This is using the (current) edit link to the page. So, if you were to save again, this would be hard-coded into your page.
Fix(es): 1)For now, only edit articles from the admin area OR if editing from the front end, always replace the <fb:like ... markup with the {} JFBCLike tag.
2) We'll be updating the plugin (again) to prevent replacements of tags on certain pages or areas: Iif task=edit, on content articles for example, or possibly just if it's in a textbox at all.
Hope this book of a post helps get you going (albeit with some workarounds). Good luck, and sorry for your troubles.