In the case of the flaps example, the answer would depend on my view of possible assymetric flap situation, which would probably be lethal.
On the TB20, it "cannot" happen because there is a shaft that joins the two together.
On a short flight, say 200nm, and at low altitudes, say below FL100, I would probably fly on, but it does depend on various factors. If it was just a fun flight then I would return and get it fixed at the convenient place I am based at. It would probably be a flap motor / relay fault which is fairly easy to fix. If it looked more sinister I would return immediately, without touching the flaps.