In sum, owners of the Mazda 3 Infotainment System are experiencing a lot of issues.
Among the issues that I have experienced are bluetooth music playback cutting in and out, USB not recognizing devices, the system shutting down while driving, and ticking upon USB playback through my iPhone.
Other symptoms from various other owners include complete and total loss of all functionality of the system, including the radio.
The software is currently on its 33rd iteration. I view this as a sign that Mazda has a very buggy system, but I digress.
In any case, I have isolated the USB playback issue to the phone OS. It appears that the Infotainment System does not like iOS. The issue occurred in iOS 7 and iOS 8 across two different iPhone 5s's and one iPhone 6 Plus. I have done all of the following to isolate the issue for the dealer, who has been less than helpful until I called and complained with a sales manager:
erase/reformat the phone, installing only a few songs to test with and no other software or user content: issue persists
replace the USB to Lightning cable: issue persists
test same phone and cable in 2013 Dodge Dart: no issues
test another phone: issue persists
test 3rd party cable (Tech Armor): issue persists
test flash drive: no issues
I wanted to bring this information over here in case someone stumbles upon it and they find it helpful.
After I complained to the sales manager, he got me connected with the service manager, who was eager to help me. He got a tech to submit a ticket of some sort with Mazda's Infotainment engineers. The latest I heard from him was yesterday, and he told me via text message that the solution may take a while as it appears that the issue is bigger than simply my car.
Seems to be a common problem. Forums are filled with similar problems, love all the new tech toys cars are coming with but damn if the quality assurance isn't there.