Sorry for the delay in getting back to you on this question.
First off, great looking site!
As to your issues, I'm not sure why that's happening. The best, quick, suggestion I can have is to go into the JFBConnect Social configuration area and set the social buttons for K2 - Like to show in all categories with no articles set for inclusion or exclusion. Basically, set it to show on everywhere and see if that works.
If it does show properly, then slowly add exclusions (per category or item id) for the areas you don't want it to show.
If it doesn't show properly, try adding the specific K2 item ID to the inclusions field, and see if it shows properly.
If none of the above helps, we'd recommend trying to disable your SEF extension temporarily (assuming it's sh404SEF). While disabled, try navigating to some of the good and bad pages and see if there is any difference in behavior. It's possible that the SEF extension is altering the URLs in a way that we can't detect the type of view. If that doesn't help, please post a 'good' URL and a 'bad' URL in the non-SEF (index.php?option...) form. That may help us debug further.
Thanks,
Alex