One problem related to battery has been reported for the 2008 Mazda MAZDA3. The most recently reported issues are listed below. Please also check out the statistics and reliability analysis of the 2008 Mazda MAZDA3 based on all problems reported for the 2008 MAZDA3.
I started the car, put it in reverse and began backing out. As the car began to move the steering felt sluggish like the power steering was not working. The condition lasted a few seconds then cleared up. That happened twice more as I was backing out. Whenever the steering became sluggish some of the warning lights turned on (low tire, abs, brake, oil, etc). They turned off whenever the steering returned to normal. The condition seemed to clear itself so I put the car in drive and went a few hundred feet. The sluggish steering and flashing warning lights began again. I stopped the car, left the engine running and checked the tires, power steering belt, and power steering fluid level. All were ok. At this point I shut off the engine and removed the key. The speedometer and tachometer needles oscillated wildly from end to end for several seconds. The warning lights were also on. After waiting for the instrumentation to settle to the normal off state, I inserted the key and attempted to start the vehicle. There was no electrical power whatever, like the battery had been removed. I removed the key waited 15 seconds and attempted to start the engine again. That time the car started as expected. I drove the car slowly for a few minutes and there was no recurrence of the problem. The car has been driven several hundred miles since then with no recurrence of the steering issue or flashing warning lights.