Trust me, no matter how careful I am, my cut out pieces are never perfect either. You just do the best you can. It could be that you need to use more straight pins and place them closer to the edge. If you’re using a silky or slippery fabric, try using my tissue paper trick that I discuss in the tutorial working with Silk and Silk-like fabrics. Also, another option is investing in a rotary cutter and cutting mat. That way the pieces are always lying flat and not getting shifted. If you do use a rotary cutter to cut out your pieces, make sure that you get a small blade as those go around curves easier. Hope this helps.