I have ridden BART most workdays for the past 7 years. I have encountered trains with stuck doors a several times, and on none of those occasions was the train put out of service. In fact, they even have pre-printed stickers that say something to the effect of "This door is not working; please use other door." I have seen these perhaps half a dozen times since I began riding BART regularly.
Note that these doors were stuck _closed_. It would be an obvious safety hazard if the door was stuck open - in that case I can well imagine that the operator would not move the train from the station.
This has happened a few times this year. Although the video is dated April 1, I can vouch for the authenticity; this is my neighborhood line and I have gotten used to the recurring problems of particular rail carriages. If it were up to me I'd scrap the light rail on the west side of the city and put in buses instead.
I've ridden Muni only a handful of times. On one of them, a homeless man threatened to cut my throat with a knife. Admittedly, it was because I stepped up when he began screaming at a non-white person (Middle-Eastern, perhaps, with some variant of head scarf) and her toddler.
> One door on the #BART train gets stuck, the entire train is out of service. Hundreds of people out onto the platform! #incredible
https://twitter.com/#!/mjijackson/status/100612825134800898
I had that same sort of thing happen to me in Phoenix, but people don't take public transportation as seriously there.