it's not necessarily all fake paths -- it's more identifying what the player will likely do and trying to force them to use the mechanic in a way that's surprising. i like to write down all the corner cases i find while i'm testing the game and then try to build puzzles around those cases.
iteration is also very important for puzzle design. i test a lot and try to improve puzzles i'm not happy with, and cut out ones that will never work.
for the 1,1 coin door, it is impossible to get normally (you can't jump the spikes). you have to use another of your abilities. :)
