Modern subways have interlocks preventing motion while the doors are open, and preventing the doors from opening while the train is in motion.
Yeah, until the drivers decide that the doors are so unreliable that it's faster to override the interlocks and hope nobody's caught in the doors (which will eventually reset themselves and close properly).
On Muni's older Breda trams the interlock had a little toggle switch on the circuit breaker panel (conveniently located in the cab) you could use to override it. On the newer ones, it looks like the doors didn't detect a "pinch", the interlock decided the doors were closed enough, and the driver couldn't be bothered to check the video cameras.