So I've just had my first take on a PCB (used an acetate paper) and made some corrections afterwards with a marker pen. But as I am not that good at drawing, some lines are uneven widthwise. (It's getting thinner or thicker along the line) Can that be a big problem in the function of the circuit?

 

Shouldnt be a problem unless you draw too much current through too thin trace.

 

Not a problem unless you create shorts.