From a statement released by Pirelli detailing the causes of the tire failures at the British GP:
"Rear tires that were mounted the wrong way round: in other words, the right hand tyre being placed where the left hand one should be and vice versa, on the cars that suffered failures. The tyres supplied this year have an asymmetric structure, which means that they are not designed to be interchangeable. The sidewalls are designed in such a way to deal with specific loads on the internal and external sides of the tyre. So swapping the tyres round has an effect on how they work in certain conditions. In particular, the external part is designed to cope with the very high loads that are generated while cornering at a circuit as demanding as Silverstone, with its rapid left-hand bends and some kerbs that are particularly aggressive."
My first job was mounting and repairing tires when I was fifteen years old. I never once made the mistake of mounting a tire backwards on a rim or from left to right. I find it hard to believe that the professionals who mount these tires on the rims (Pirelli or the teams) or mechanics from Toro Rosso, Ferrari, Mercedes, and McLaren all making the same bone-headed mistake during pit stops.
Pirelli, I'm calling bullshit on this excuse. It's time to own up that you've engineered sub par tires — either through willful negligence, incompetence, or pushing the envelop too far with regards to tire degradation.
Multiple tire manufacturers cannot arrive soon enough (despite regulations to the contrary and the looming deadline for the 2014 season).
EDIT: It appears the teams are intentionally mounting the tire on the wrong sides, changing the thermal characteristics and tire behavior to an advantage. Holy crap. My point still stands about Pirelli needing to take responsibility and calling for a tire war.