I can say with 100% certainty, that for some people, 1mg might cause side effects...
Why do people expect end all, be all answers from a board of generally inexperienced users? Do some research... a quick google will yield a list of side effects and WHY those side effects exist, then you can decide for yourself.
Propecia is a 5Alpha reductase inhibitor, it basically blocks conversion of test to DHT... dht is one of the strongest androgens found in the body, therefore, yes it CAN have sides for some people, most notably sexual side effects