Miamian here. I don't think Miami is any different from any other large city. Of course there are a few dangerous areas of town that you should avoid at all times. There are also great neighborhoods for families that have a very safe feeling. You must always use common sense when out on the street.
If you are in the heart of the party district on Miami Beach late at night then yes, there would be some risk for pickpocketing, mugging or whatever. Cars can get broken into anywhere. Like I said, it's a big city and that is not unusual, unfortunately.