Strange electrical issues '12 Mazda 3 Skyactiv

I've recently run into a few odd electrical issues in my '12 Mazda 3, not sure if anyone else has seen these problems with their cars or not...

1. Headlights are flashing/pulsing when I brake. I put in a new battery because the OEM wasn't up to the task of reliable starting in the brutally cold Wisconsin winter. Checked and double checked all connections, everything is good and tight. The ground to the body looks fine too, I don't see any other signs of the battery being bad, though I may take it to have the battery tested to ensure it is OK. My next step is to swap back batteries to see if there isn't an issue with the Optima red top I put in.

2. Cruise control won't engage intermittently. This has been happening for a few months, and it just randomly occurs. Happened yesterday, which was the fourth time in two months. This morning on my drive to work, cruise engaged just fine. What happens is that the yellow light for cruise will come on, but when I hit the Set or Res buttons, nothing happens, the indicator light never changes and the cruise control fails to engage.

Anyone else encountering strange issues? The second issue, I can live with, if you restart the car it typically goes away, but the first issue seems like a hazard.

Dealership was able to resolve the issue that was causing the lights to flash. The alternator was not putting out the correct voltage under heavy battery load, it required a reflash of the PCM. Service Bulletin 358886, for anyone who stumbles across this. They fixed this as a courtesy, even though I am out of warranty.

The cruise control remains a mystery, and since I'm out of warranty already, it might go unsolved.