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Maszek,
Each case is usually different, but we probably could have some 'common conflict' notes. Thanks for the suggestion. We always try for top-notch documentation, and love recommendations for when we might be falling short.

As for your issue, looking at your page, you're using a different Like button than the one provided with JFBConnect. If possible, we'd recommend switching over to using our JFBCLike module or the {JFBCLike} tag, depending on what's easier for you. The reason there is a conflict is because the other Like button you're using is re-including the Facebook Javascript API library (search your page for 'all.js' and you'll see it). This 2nd inclusion either needs to be removed from that module (sometimes a parameter, sometimes it has to be done manually) somehow.. or simply switch to ours.

If that still doesn't fix your issue, just let us know, and we'll gladly look into other possible causes, but that's definitely the first step. I don't see anything else obviously wrong with your site.

Thanks,
Alex