Regardless of the cause, this video gave me chills when I first saw it:
https://www.youtube.com/watch?v=j2ItrwJ1zuc
It looks like a 2nd gen, at least from the dash. Could be underinflated tires, overloaded, combination of both... who knows.
I think a lot of the issue came from the fact that this was a lighter SUV that people treated like a sports car due to it's size. You don't see this happening with Suburbans or large trucks. The Explorer feels more like a car than a truck. The tire pressures were definitely too low and putting passenger rated tires on probably didn't help when people overloaded them.
It has to have some blame with the drivers & the tires because a lot of the handling characteristics and geometry were made with the earlier Rangers & Broncos that came many years before the Explorer did. Granted, those were 2-door but still, if it was a major inherent problem in design, these issues would have come up sooner.
Living in a rural area, it's shocking to see how many people just don't care about their vehicles. Balding tires and low air pressure, leaks & suspension issues. I'm fully aware that vehicles, especially older ones, take money to fix, often more than you want to invest but it's really hard to put a price on reliability or better yet, your life. I went through the whole tire thing myself. My Explorer came with 8 year old balding chinese tires that were dry rotted and had splits in them and I drove it that way for a year until this winter came. Something had to be done because they didn't have enough tread to do anything in the snow. I got some used mis-matched tires of varying tread and age and had them mounted. One went flat a week later, another started showing sidewall bubbling. I broke down and bought a new set of Coopers. I didn't want to fork over that $500 but now I have reliability and safety. They handle so much better and in 4x4, it crawls over anything. Looking back on it now, I feel stupid for not doing it sooner. You just cannot cheap out on critical things like this. The entire performance of the vehicle depends on the tires.
Another reason Explorers were called Exploders, and I think it might be the primary reason, was that the 2nd gens had an issue with the cruise control switch in the brake system. It was submerged in brake fluid, in the reservoir if I recall right. The switches were faulty and started fires. This was a problem on a lot of Fords though, it was the design of the circuit itself. The sensor was live 24/7, even with the engine off and key removed.
http://www.cnn.com/2005/US/06/16/ford.vehicles/index.html