One problem related to battery cable has been reported for the 2013 Mazda MAZDA3. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2013 Mazda MAZDA3 based on all problems reported for the 2013 MAZDA3.
Driving 60mph on major freeway during rush hour, light rain. Check engine light came on and stayed on. A few minutes later, every warning light came on and I lost the power steering. I pulled to the side of the highway and turned the car of, waited 10 minutes and started the car. Check engine light remained on and all other warning lights were off. Started driving and 10 minutes later all the warning lights came on again and lost power steering again. Left vehicle in garage over night with hood up thinking it was due to rain/moisture/computer problem. Car started fine in morning, no warning lights. Took it to dealership and they said it was a lose battery cable. I am thinking it was more than that. I have noted my concern and will await the next heavy rain.