I have seen the Flight Status page show Delayed when the expected departure time is less than 5 minutes later than scheduled. Tracing the flight upstream I saw a somewhat larger delay, and that larger number proved more accurate.

As to why airlines post optimistic times, that's simple: if things go very well they don't want to be choose between taking the originally estimated delay or leaving without passengers who believed the earlier estimate. By convention, a posted delay is a "no earlier than" time, which is exactly what you need to know if you are going to grab a bite to eat, for example.