With papercut animation, it isn't as costly as amateur stop motion, but it still has the same problems with scenes and key frames. The main way that I have found to target this is to use tracing paper to map out paths of motion, this way you don't lose track of where your character is going. In this diagram you can see it's showing to use a circle to plan out the motion of the cats head.
Squash and stretch can also be slightly lost with cut out, it could still be done by making different paper puppets stretched out for affect. However, with 2D animation squash and stretch can easily be achieved and played with as much as desired. It can be argued that squash and stretch isn't used as much in cut out as it loses the effect of a solid object.
In every new frame within stop motion the frame has to be redone by hand, which could be technical limitation. When looking at 3D animation the animator can create key poses and the computer will create the inbetweens for them, whereas this is not possible within stop motion or papercut animation.