Doors...
I seriously doubt that a UNITED flight departed with the doors open....
but you may have flown on UNITED EXPRESS which, depending on the aircraft, may not have had a cockpit door installed.
If it is United Express, please remember that you are not flying on United, but a contracted subcarrier who cannot afford services like a reservations system. The paint on the aircraft may be the same, but.........
It would be nice if you would email me the date and flight number; I can search the computers and tell you more about your flight.
Merrry Christmas