I have a couple of suggestions for you...
1. Use some very light stabilizer behind the area you are applique-ing. It helps.
2. Turn your tension down a little bit.
3. Make your zig-zag a little bit longer than you would think. Not too long, not too short.
4. Sew slowly until you really get the hang of it. My first machine applique project was amazingly slow...it took me over 1 hour to sew down the first piece. By the time I finished I was down to about 10 minutes per piece. I'm faster than that now, but it takes a lot of practice to really get a rhythm down, and it depends on how detailed the edge of your pieces are.
Keep at it...you are doing good for a beginner!!