First of all, more pins! I pin every two inches or so when hand piecing.
Next, try sticking all of your pins in horizontally before securing them vertically. That may help you keep everything lined up.
Also, lay the hand holding the fabric on the arm of the sofa or something to keep it stationary while you sew. This should reduce any strain you might be putting on the fabric that's making it lose its shape.
Finally, wash the quilt when you're done and you'll never, ever see anywhere those seams aren't perfect.
