They’re triggered whenever Beeminder gets a new datapoint and nothing happens when they fail. If you wanted it to be super robust I think you’d want to periodically sync it with the datapoints endpoint of the API. The format is JSON and should be pretty self-explanatory. I’d recommend just setting the callback to something that echoes what it receives and then add a test datapoint to see what gets sent.
As for code that parses callbacks, check out Paul Fenwick’s Exobrain.
I’m guessing we don’t quibble about self-signed certs but I guess that too is easy to check. Let us know if you think we’re doing the wrong thing in that regard!
PS: Curious to hear what awesomeness you’re cooking up!
PPS: The original idea for this callback feature was to enable PESOS – keeping a realtime mirror on your own site of all your Beeminder data. It has turned out to mostly be useful for other, even awesomer, things.