Keep in mind this car is designed with performance in mind and things like reliability are secondary (like it or not).
Here are some inherent weaknesses:
(1) Overheating. By design the rotary engine puts out a lot of heat to put out the high horsepower with a small displacement. This is just how the engine was designed. The banana shaped combustion chamber is just not as thermally efficient as pistons. So Mazda put in stuff like oil coolers, big factory radiators, 3 catalytic converters, and air pump to address this and the emissions problem. Funny thing is these are still trouble spots. The oil line leaks, clutch fan no longer works, and water jacket blows, are examples of this. Next thing you know you need a new engine because it is blowing out coolant. It is imperative that the oiling and cooling system is kept in good shape in these cars. They are more sensitive to these failures than piston engines.
(2) Flooding. This will leave you stranded and will eat several batteries and starters in the process. It happens when you start the car, then shut it down without it properly warming up. There are lots of discussions on this topic, but it is definitely annoying. You basically have to purge all the fuel by removing spark plugs, cranking several times to purge fuel, reinstall plugs, crank again, etc.. There are detail procedures in several websites, but anyone owning a 2nd gen will know what I am talking about. This is definitely pathetic in the age of sure fire fuel injection.
(3) Clutch pilot bearing. This needle bearing has no inner race and actually rides on the input shaft of the transmission. As a result, if you ride the clutch a lot, then it will eventually fail and you won't be able to shift into gear. I blame this on bad design of transmission. It would have been actually more reliable to put a bushing in there instead (as other manufactures do) or better yet put in a real bearing.
(4) Hard shifting transmission/bad gears. Again bad design. This applies to all non-turbo transmissions. Mazda basically carried over the transmission from the 1st gen (a lighter car) without a new redesign. You can tell because there are a lot of similarities like same input shaft diameters and same needle pilot bearing. Well when you use a design meant for a lighter car and use it on a heavier car, it does not take a rocket scientist to figure that there will be problems down the road. Let's just say that the transmission needed work before 100k miles. Note this is a separate issue from the pilot bearing one.
(5) Electrical... stuff like Logicon and CPU can be on the fritz due too bad solder joints.
(6) Window wiper intermittent no good due to a bad relay. This can be a problem because state inspections require them to work at all speeds (stupid law).
(7) Bad trim. The window sill trims tend to rust. The inside overhead trim cracks.
(8) Sucks up a lot of gas. Engine is again inefficient. They say it'll get better with the upcoming Renesis engine, but we'll see.
Conclusion: You would have to be an enthusiast to put up with the many quirks of RX7s.