One problem related to horn assembly 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.
Horn gradually failed, became weaker and weaker, eventually totally silent. Looked on google to find location (it is very tight in there!) discovered numerous complaints of failed horns for this exact make and model. Horn is made by fiamm (italy). Examined horn, the adjustment screw is sealed. Failure is internal. Vehicle is two years old, has 39,000 miles. Replaced horn with $10 aftermarket item, all ok now. Took me about 45 minutes to do, and I am an experienced mechanic (cause is absolutely miserable access, only had to remove one nut and one wire, the trick is getting to it), I fix everything from wristwatches to airplane engines. No accidents, no injuries, but you must have a working horn . . . This is my wife's car, and I want her to be safe.