I've never heard anyone say they were there when the divers were not performing. And even with 3 ships in port, there is plenty of room to see them. The more tourists there are, the more money there is to be made, and the more often they dive.
Most itineraries I've seen give you 8-10 hours in Mazatlan, which is ample time to see all the sights, shop and even have a shrimp feast on Stone Island or in the Golden Zone.
It is about 20 minutes to the Golden Zone and Aztec Theater from either the ship or Old Mazatlan. The going rate for one of the open air 3 passenger taxis is $10.00.