The controls need to be a bit tighter. Brackeys made a video on this (look for 2D movement in unity, on youtube).
It is very frustrating when your character doesn't jump when you press space, or when it gets stuck on ledges. The level design is a bit ruthless, when you start to reach the top it seems that certain platforms vanish on you with no way to get back up. If at least the controls were a bit less frustrating it would be easier to circumvent, but as they aren't, it ends up being super frustrating when you're near the top.