Are you someone who sews? I consider myself someone who can sew to save my life. You'll also notice from the pictures that I don't have a new-fangled sewing machine. That's OK, this one is my grand mom's who is my inspiration for being a crafter and wanting to share what I learn.
With these small pieces with lots of curves you don't want to be in a hurry. That won't solve every problem but it will help. Back stitch when you start and when you stop. You can use the pressure foot as your guide because you aren't leaving a big seam. When you finish sewing a piece, turn it over. Look for places that may not have sewed right. Just run the machine over these places to catch both pieces of material. If the pieces are badly misaligned rip some stitches out and re-sew.
Above I'm sewing the body. I've started with the opening at the back and I've stopped at the top. Can you see I have it marked? Remember I said that there are two types of bodies, open at the top and closed at the top. This one is closed but I need to skip a couple of stitches where the head will go so that I can join the body to the head later. Your pattern should mark this place and you would mark the fabric. I literally sew to the first mark, lift the needle and move the fabric one eighth of an inch. Then proceed with your sewing. If you had an open topped body you wouldn't sew across the top. Your pattern would reflect this.
Remember you are not sewing the bottoms of the feet and ears. I'll be going over the bottoms of the feet later. I sewed that one place on the head from the nose to the neck. We'll talk about the head next. That will be a page in itself!
One last recommendation, several years back my sister broke a needle on her sewing machine and a part of the needle wound up in her eye. Because of this we both now wear glasses of some sort when we sew.