I might have made this too broad but I think this applies to all intersecting plane models. Simplest example, and the one I have actually tried, is the XYZ square.
Image from happyfolding.com
You can even see the yellow component face towards you has wrinkles. I would conclude that was the last one inserted to complete the model. Also the red paper pouch is a little bowed out from the insertion process.
I had a tough time getting the last module in and ended up having to use implements to hold parts open so that I could try and slide in the last piece. I usually also use scissors to make the flaps (that you will see below) smaller to insert it easier. Instructions for this specific model can be found here. In the instructions the last steps are apply described:
[A]ssembling the first 4 units is easy, last two are difficult
It looks bad when it is done by me. It is possible the paper has something to do with it. I made my model from 4" square origami paper stock. Is there more advice I could head for models like this?