The problem with Delta's system (and probably other airlines'), at least in Atlanta and I'm sure it's the same at other airports, is that they don't always mark the flight as delayed in the computer system, and even though it's delayed it will disappear off the screen as if it has departed on time.

I saw this behavior on a flight I was on just a few weeks ago. Our flight was delayed about 45 minutes, but it was not shown on the screens as delayed, it was not shown on the screens at all since the computer thought it had already departed.