> Would I have a chance of running a very low frequency PIC16
> on this type of supply? would i need to stick a 7805 in too? or
> is it simply too noisy?

They can be made pretty clean, more like this

http://home.clear.net.nz/pages/joecolquitt/txless.html

The X2 capacitor determines how much current is available, up
to you how much filtering you need/add

Wouter said -

"The other problem with this type of circuit is the voltage on the
mains plug after uplugging..."

A suitably-rated bleeder resistor would fix that

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