Why did they say "come down"? It sounds like you have to come down from upstairs to downstairs, but isn't it related to height but just "come over"?
-Ghost whisperer
Hospital : This is mercy hospital. Your husband's been in an accident and we need you to come down as soon as possible. Do you know where we're located?
*Not a teacher
As far as I know, come down is also used when you come from a big city (usually a residence) to a smaller city.
Come over might sound too casual and come here might sound too bossy, so come down fits in the middle- it's polite but pressing.
1. It has no vital meaning. The utterance could be made simply as Your husband's been in an accident and we need you to come as soon as possible.
The context would make it clear that the 'coming' meant 'to the place from which I am speaking - Mercy Hospital'.
2. I agree with SirGod. 'Come down' can also be used in that way, but I don't think that's a likely reading in your example. If it had been, the speaker would have said something like, "This is Mercy Hospital in X" (X = the name of the smaller town).
noteacher
They could as easily have said 'come up' to the hospital. Maybe it's on a hill.
Come down could imply that the hospital is downtown, but it's probably just generic usage in most places.