You have to turn off "Tap to click" in the touchpad preferences. I can't remember if it is on by default or not, but it's the one thing I can't deal with. Any sort of accidental brush acts like a click and that's annoying, which sounds like what you are complaining about.
It's not on by default, which is what puzzles me about slantyyz's comments. I can't imagine anyone finding clicking and dragging more difficult on a macbook than on another laptop.
I find clicking and dragging more difficult on laptops without physical buttons (Macbook and Windows) than laptops with physical trackpad buttons. YMMV
