A) leave myself a little extra time getting to the airport
B) watch the incoming aircraft rather than posted times of my own.
As I got to PHX Terminal 3 at 4:50 for my 6pm flight to LA (with 40 min to make my connection to SFO there, including taking shuttle from American Eagle commuter to main terminal) I realized that even though it was showing on time, incoming flight was already 50+ min late departing LA!
And the flight I'd be connecting to is last SFO flight from LA on AA.
The first agent I pointed this out to said "no, no 3805 is on time at 6pm" - I had to ask her to look at 3806... "Hmm - arriving 6:06pm...". Now she asked one of the other agents to rebook me.
I had *just* enough time to convince them to push my ticket to USAir non-stop at 5:50 rather than the UA LAX-SFO flight which would require additional security clearing in LA and I ran for bus to T4, got a new boarding pass from the machine, stood forever in security, got the pad-down, grabbed a pretzel and got to my gate as they were boarding Zone 1 :)