Any problems driving an LED from the mains using a blocking cap as a
constant current source?
There are two to deal with:
1: Inrush current - easy to solve with a series resistor to limit that
to something that does not damage the LED.
2: Reliability of the capacitor and safety of the capacitor failing
The capacitor needs to have a decent AC voltage rating. A DC voltage
rating significantly greater than the peak voltage is not sufficient to
survive prolonged AC, even without any voltage spikes. Things get better
if the capacitor is UL recognized or the like.
One thing that also helps: Have everything enclosed in an enclosure
made of flame retardant plastic or the like, suitable for containing
things going wrong. I would not consider chances of the current
limiting capacitor failing being reduced to zero.
The resistor being used for limiting inrush current should be a
flameproof type, preferably UL recognized or the like.
I would avoid filter capacitors, since they could receive full peak line
voltage plus some of any voltage spikes if the LED(s) fails open.
Electrolytics including tantalums could leak conductive liquid if
overvoltaged. This is a concern especially if things going wrong includes
the current limiting capacitor failing short - even if only temporarily
shorting.
Sounds scary? How about using an LED that gives you enough light at a
current low enough to make practical use of a resistor without a capacitor
for current limiting? There are quite a few LEDs that are plenty bright
for use as indicator lamps at currents anywhere from .2 to 1 milliamp.