Is this transformer-less power supply a good idea?
I've used this type of design before but it should only be used with care and packaged in such a way so that nobody can easily access any connections - all connections have to be regarded as lethal.

I would add a current limiting resistor in series with the input capacitor because you cannot rule out fast transients occurring on the incoming AC supply and this could cause very large current peaks and potentially destroy the zener and then you have a knock-on problem if it goes open circuit.

Clearly also your diodes need to be rated at the correct reverse potential for AC mains in your neck of the woods.

C1 does seem excessive at 3uF - it's impedance at 50 Hz will be about 1000 ohms and, from a 230 V AC supply will draw a standing current of about 220 mA RMS - that's quite a lot of bad power factor load but if it's a one-off then probably OK.