You can't walk directly off the ship in Mazatlan - you'll be shuttled through the industrial port for a short 5 minute ride. Once you reach the drop off point, there's a touristy market to explore. When you've finished checking out the local items, if you go the right direction, there's an easy and interesting walk. I made the mistake of turning to the left, and spent 30 minutes hiking a construction zone. Instead, as you come out of the shopping bazaar, stay a bit to the right, and watch for the blue overhead gate that marks the beginning of the "Blue Line". Follow the blue line, painted on the streets into the downtown market plaza - the Centro Historico -, about a mile away.
The walk starts through a residential area, then down a commercial street, until you arrive at the older part of town. Once there, you can explore restaurants, churches and markets. I'm not sure if it made me feel better, or more concerned, but there were police cars stationed prominently along the route.
Mazatlan has a very active group of expats who meet each cruise ship, and they are stationed on most every corner, available to answer questions and share their stories.