Well, there is a lot that is true in that and a lot that is just bullshit boosterism. I happen to know a pretty fair amount on this topic and will try to get as much into the 20 minutes I can use before my next meeting to address it.
Okay, a whole lot of questions, from a professional civilian.
(a) What were the significant differences between a Sherman tank and a Soviet T-34; one has the impression they were very much alike?
They really had almost nothing in common, either in design or in the doctrine they were designed to fight under. The Soviet tank was NOT American-designed, the suspension and other general design aspects was however a much-improved version of that on the Christie-based BTs (Bistrokhodniy Tankiy, or "Fast Tanks," which were obsolescent by 1941). Both appeared in variations of cast and welded construction, both had a gun in roughly the same caliber. American pre-war doctrine (Pursued until 1945) called for enemy tanks to be engaged by very lightly-armored tank destroyers with high-velocity guns, while tanks were to be used to break through where enemy tanks were not and engage everything else with lower-velocity general purpose guns. Russians used a single vehicle, the T34 for this (As we have since the dismal failure our WW2 tank doctrine induced), and the T34 was designed with a vastly superior ballistic shape. The T34s suspension gave it not only superior off-road capability, but also higher road speed, though using a dry-pin track that did not last as long as American rubber-bushed track. Your source does not go into it, but while dry-pin track is considerably shorter-lived, it is also much easier to repair or replace in the field. The T34 used a diesel engine, while the Army's Shermans used gas, or even aviation gas in the radial-engined models (Many engine and suspension variations over the production life of the Sherman); Diesel fuel is far less volatile, and the gas fuel is what earned the Sherman its nickname of "Tommy-cooker" against the Afrika Korps.
(b) A by-then-antique British Centurion tank has been the only tank I myself have ever seen up close, and operating (although not in combat, of course); how did that tank compare with the Shermans and T-34s?
The first Centurions went for field trials in 1945, and remained in service through the lifespan of the post-war M46/47/48 US tanks, the later variants armed with the same 105mm M68 cannon that was on the M1 Abrams before we switched to 120s, and the Centurion weighed 10-15 tons more. It's like comparing a Tiger (After adding hydraulic power traverse, gun stabilization, and a reliable transmission) to a Sherman or T34 - no match.
(c) One gets the impression the Allies did in fact have some heavy tanks, comparable with the German Panthers and Tigers, but not a whole lot of them; some, but not many. What were such equivalent tanks? Did they demand a vastly different training and skill to use, as compared with Shermans, or only a little bit different?
In the US case we never did get our stuff together due to the resistance of many senior officers who generally go unnamed in the accounts, though one gets the impression Patton was one of them. The M26 Pershing was fielded for combat trials in the last couple of months of WW2 in Europe and saw action, including a few engagements with Tigers. It had some transmission issues, but with an altered transmission became the M46, the most advanced tank of the Korean War. The Brits had many projects, some good and some bad, but mostly Mediums; the Centurion was the Brit equivalent of the Pershing in size and timing, it also appeared for combat trials shortly before V/E Day but a bit later than the Pershing as I recall (Armed with the 17-pounder) and I do not recall that it showed in time to actually fight any German tanks.
(d) Why did tank tracks, formidable-looking things, last only 2,500 miles, or in the case of German tanks, 500 miles? To this professional civilian, such tracks look virtually indestructible, good for a trip to the moon and back.
There is friction every time it moves on the pin. Americans used a rubber bushing between the pin and the track shoe (Expensive and dependent on rubber), about everyone else including the Brits generally used dry track (Steel pin through a steel shoe, or "Dry track"). There is a lot of stress involved in moving a 30-50 ton tank around, and in abrasive dust and sand at that.
(e) If the Soviet-made T-34 was the "best" tank of the war, why wasn't it adapted by the Allies, too--and remember, apparently the T-34 was American-designed in the first place.
It actually wasn't American-designed, any more than the V2 was designed by Robert Goddard. We had our own way of doing things, and pursued technology on those paths to a viable end (eventually). As large as our acceptable casualty rates were, the T34 was designed to fight for a nation where even bigger ones were not just acceptable but the norm.
(f) What is the current equivalent of the now-obsolete (one assumes now-obsolete) Sherman tank--light-weight, fast moving, smaller, but not so well armored as heavy tanks?
Doctrine is pretty different these days; since the late 50s there are only main battle tanks and "Other" armored vehicles. I could explain at length why it's better, but I'm out of time.
