Alright, after pouring in too much time into this game, I have found quite a number of glitches. My device is an Ipad Air on version 9.3.2.
In Chapter 1, in the area where you grab the second puzzle piece on the cliff, you need the egg pencil. To get back down, you're supposed to hatch another egg on the bottom, then stand on the feather on the cliff. But, instead you can glitch over the cliffside by walking left of the top feather.
In Chapter 2, you need to help the scientist collect four gems to create a potion to advance. But, I'm quite supposed that no one else had reported this, you could glitch through the black line/tear and the rock behind where the scientist is originally standing. By having your character walk up into said rock and line, they will start to levitate. After that starts to happen, have your character walk in a diagonal, up and right. If you're lucky, you'll pop right through to the other side without needing to help the scientist at all. This would make for a great speedrunning tactic. Otherwise, you'll get ejected from the wall, back onto the ground. When it does eject you, you can direct your character to land on top of the minecart nearby.
I'll post more below this, as I'm having difficulties trying to submit the whole list in one post.