1) The owners who treat the rotary engine like a piston engine. This isn't an engine you can simply ignore. There are no special tricks to maintaining one, but the engine MUST be looked after. Run the engine to redline at least once every couple days to keep carbon build-up at bay, and change the oil and coolant at the times specified. No slacking
2) Mazda Techs who say the car is bad because they haven't got a @#%&* clue how to work on them...'nuff said about these idiots... Find a GOOD Mazda dealer (preferably one involved with Mazda Motorsports if you can) while on warranty. After that find a good, knowledgable rotary mechanic. Check with your local Sports Car clubs.
3) When you start the car do not stop the engine cold. This can cause flooding. Always let it run for a couple minutes once started. I've never flooded mine even when it has stalled cold, but it's good advice nonetheless.
4) Moisture in the tail lights have been a known issue. There is a TSB out about this so warranty repair is available is this is an issue.
5) "Clicking" from the front end when you fully crank the wheel. TSB is out on this, too.
6) Brake squeal. Mainly caused by being too gentle on the brakes causing glazing. Braking hard once-a-day should keep this at bay. TSB issued anyway.
7) Sun visors breaking caused by excess heat in car during hot summer temperatures. It softens the plastic.
8) Premature Catalytic Converter death. Under EPA warranty up to 100K miles in the US, I believe.