I just recently picked up a CST L-TracX, and for the first few days, I had the click/drag issue blue mentioned.
But really, you do get used to it. It also depends on the trackball though. The CST has HUGE buttons, so it's easy to hit them regardless of where your fingers are on the ball.
Since you said hitting with your thumb, I assume you have a "fingers" trackball, rather than a thumb model. Good choice!