Join the club. My family circumstances have meant over four years of transcontinental travel three to five times a year. All of this traveling has meant a lot of stressed-out airborne hours, a lot of supportive flight attendants, and a lot of commiserating with other traveling parents. I've divided up my experience into three sections. After that, I'm told, you reach a glorious period where the kids are reasonably content to play Game Boys and watch the in-flight movie.
Every transfer adds peril.
Never go first class. The last flight before a red-eye tends to fill up. If you buy a seat for your child, ask for the aisle and window seat on planes that have three-seat rows. Fly so that your child's normal naptime coincides with the middle of the flight. Consider, also, time changes and jet lag.