Hi Jamie
THis past summer I built my own picket fences but I didn't use pallets. I used wooden lathes that I was also able to get for free from Home Depot. My fences are really border fences around various flower beds not full size picket fences. The best advice I can offer is to measure the area several times before you start putting it all together. I laid my pieces all out where I was going to put them before I actually started putting everything together. Once I had it all lined up the way I wanted it I marked everything so that when I started putting it all together there wouldn't be any guesswork. This spring I will be building a picket fence to go down the side of our front yard between my neighbors house and ours for more flower beds.
I wish you the very best of luck.
Penny