I wasn’t seeing any of the usual JS errors in the console in Chrome either, which was a bit confusing, at least until I opened Safari and saw this:
Uncaught RangeError: Maximum call stack size exceeded
According to this question on StackOverflow, the problem is caused by running the old Facebook SDK (FeatureLoader.js) alongside the new one (all.js). I was positive that FeatureLoader.js wasn’t loading anywhere in my codebase, and a quick check with ack didn’t show anything either. FeatureLoader.js definitely was getting loaded though, and when I double-checked I saw that it was being loaded by a locally-installed dev plugin that I have running (but that isn’t on our dev or production sites). Plugin removed, problem solved.