In Firefox, the Like button is checking for me and the LinkedIn & Facebook Share buttons pop open new windows as they should.
Pop-up blockers shouldn't prevent the share buttons from working, even if enabled. An 'action' by the user (clicking on a button) bypasses ad-blockers. Their whole purpose is to prevent unwanted windows from appearing.. but the user action of clicking the share button should, and does, work from my testing.
Attached is a picture of the Like button working for me as well. I just clicked it and you can see the check. In Firefox Preferences -> Privacy & Security, my setting is 'Standard', which is the default.
Sorry I don't have any specifics as to what may be happening on your system. I can only suggest trying from Firefox on different computers or different networks, which may have different firewalls or ad-blockers setup to see if there's some common thread causing the Like button to fail.
Thanks,
Alex