I'm stupid with electronics too. Generally, if I build anything with mains, I hide behind the chair the first time I switch it on.
The obvious thing to test is the voltage across the LEDs. You'll probably want to attach (and double-check) the probes before turning it on. If the LEDs have failed you may get mains voltage across them, so start out with the meter on a high setting. If everything is working well then you'll get 1-2V AC.
The next worry I would have is the capacitor. Try disconnecting it. The GPIO should then see a 50 or 60Hz square wave when power is on.
Also be aware of the comments further up the page that the 100K resistor looks rather large for the application. If you do have 1-2V across them and no signal with the capacitor out of circuit, I would try reducing it to 2W 50K.