Well I'll compare to one of the cars i've owned previously. A chevrolet cavalier.
1. Weight...the P5 is 2700lbs...compared to many other cars of similar, or even smaller size, it's rather light. My Cavalier Coupe, without a driver grossed at around 3400lbs, good luck finding many wagons that weigh less than a protege.
2. Suspension. The P5 is much stiffer than a lot of the econoboxes you'll find. My best friend's father owned a P5, and decided to sell it for a better riding vehicle. Don't get me wrong, he praised the P5 for great handling, fun to drive, and the ride quality (should he have been a younger man) is really nice, but his lower back didn't like the potholes in the P5. My butt says the P5 has less than HALF the body roll that heavy chevy cavie I drove...and it's about a 1 1/2 ft longer. Not to mention, Fully independent front AND rear suspension. Many vehicles have a torsion bar in the rear...which is one, heavy and two, OLD TECH. Yeah, the P5 is a decade old, but the technology that went into its suspension is the same technology mazda put into their race cars. Also, did you look at the ride height? I've had people ask me if my STOCK P5 is lowered...always a no. Compared to the cavalier, which is the epitomy of cheap econobox, the p5 is rather low.
3. The Body! Every car on the road today is a Unibody car, and structural bracing is very important. If mazda had the foresight to put a front strut bar in the P5, one can speculate that the car elsewhere is pretty rigid. I remember seeing a build on these very forums not long ago where certain components of structure were being drilled and removed with little to no adverse effect on the rigidity of the car...THAT'S A SOLID BODY. Now, a unibody car will always have some flex in the turns...but a wagon, unlike a coupe or sedan, is more "egg" shaped. Not sure if you've ever studied the shape of an egg, but it's rather strong, with fewer points of flex than a comparable sedan or coupe, and thus is more flat in the corners! Not to mention, in my experience, the components of the car are rather solid. In the chevy I drove, the most common problem was the strut mounts failing (especially on lowered cars). Mine failed, most everybody I knew who owned a cavalier, their mounts failed...this is your springs and shock absorbers we're talking about! And mounts are failing? No...I've searched these forums, due to the previous car's failures, only to pleasantly find there are very few problems with structural components of the suspension failing!
4. Brakes! The P5 comes stock with front and rear disc brakes. The ability to reduce speed quickly, while dispersing heat efficiently is one of the biggest problems engineers face when building a car. The cars must be able to stop, must be able to brake while cornering, while maintaining a range of predictability for everyday driving. Many cars on the road, to this day, come with rear drums. For most cars, that's adequate. Most cars only require 30% of the front brakes capacity in the rear to keep the car straight. More or less will induce oversteer or understeer under braking while shifting momentum. The nice rigid mazdas that have a tendency to torque steer do well with some good solid rear discs. Why? Cause the increased rear braking capacity will allow the rear to exhibit more oversteer when the car wants to understeer when momentum is pushing the car sideways. That increase in braking capacity not only allows for more oversteer in the corners, but your straight line braking with good brakes is far superior to drums, not to mention easier to maintain! And the P5, while lacking anti-lock in most models and regions, has some fabulous brakes, in my opinion.
5. Steering...it's responsive, and on a Front Wheel Drive vehicle, that is key to cornering. With the drive wheels up front, it's nice to be able to adjust steering slightly and watch those front wheels just suck that front end around. It's predictable, it's precise, and that leads to much better driving experience. Like you said, when there's dead spots, or play in the steering, wallowing through the turns is about the best you're gonna do. When the steering is sharp and responsive, you're adjusting the direction of the front end with simple, predictable movements. Not throwing the wheel from side to side just to make the car turn.
And Finally 6...it's a Mazda...Chevy likes to think they're built like a rock...they handle like one too. Honda is powered by dreams...cause they are driven by 17 years olds dreaming of Fast and Furious. Mercedes Benz is unlike any other...and outprices them too. Nissans are built for the human race, you'd think they be built for the road race? And if BMW is the ultimate driving machine...why isn't their slogan ZOOM ZOOM!? More Mazdas are driven on any given weekend than any other automaker ON THE PLANET...not because the cars are fast, but because it doesn't take a pro race car driver to be able to track one, and be able to compete.