Thank you for your suggestions! I actually did not think so much about the puzzle side of my game and concentrated more on the platforming elements, which is especially evident in the last level. I will certainly try to play around with my focus between the two sides and see, if this game should be more a puzzle, platformer or somewhere in between.
As for the dimension switch affecting things, I have not given it much of a thought. I concidered to add enemies in the future, that would attack you if you see them. Your idea about moving other things with the dimension switch is very interesting indeed.