Your water flush technique was pretty smart.

I'm not sure how I would get rid of the oil remnants completely, but I can tell you how the car would be effected: Oil remnants may enter the fluid ports (water ports) within the engine block and clog up some valves and gaskets within as well. The engine and the radiator can be compared to the human circulatory system. That oil is like the cholesterol than impedes blood flow to and from the heart. The same goes for the radiator and the engine. So, water may be flowing through your engine at a slower flow rate, thus not taking enough heat away from the engine. Your engine could overheat under circumstances where it normally wouldn't.

Unless the water current within the system is strong enough to flush or push out little oil masses within, I'm guessing your mechanic would flush out the pipes with an external source.

Funny thing I remembered about women and cars, though some guys might exhibit the same behavior:

On the RCA strip, a beater was parallel-parked in front of my friend's car. His girlfriend does not have the word "momentum" in her dictionary. She gave it one long hard push and walked off, still oblivious even after the beater smooched the back of a brand new mercedes parked ahead.

Oh, unrelated but funny: My other friend who was drunk got into the front passenger seat of a Honda Jazz he thought was his and just chilled silently. Yup, you guesed it, the owner was in the driver seat obviously waiting for somebody. She had the terrified look on her face unlike any I've seen before.