Back in the days of yore I had a 1972 Pontiac with a six cylinder. That was in 1975. I had the engine rebuilt twice and when it seized up a third time I tried a differnt approach. The engine had a serial number that corresponded to where it was made. I think it was Pontiac Michigan. I was told engines coming out of that plant had lubrication problems but the ones coming out of Detroit going into Chevy's ran forever. They were supposedly the same design. Luckily a lot of kids were wrapping there new Chevy's around trees making available many used engines. I went to a junkyard and bought one for fifty bucks out of a 2 year old Chevy wreck. It fit like a glove. It was virtually identicle. I drove the car from Long island to Morrissville for college and then for 7 more years before it went to the junkyard with a rotted frame but a perfectly good running engine. The upstate road salt did her in. In those days it did not matter. The new car warranty's were gone by the time the car was a year old. From then on I checked the engine ID's on cars I bought. Then GM started putting any engine from any plant in any car. I also remember Nassau County bought a fleet of Pontiac police cars. Within a year they had all seized up. People started finding engines out of Pontiac with generic valve covers in Cadillac's. They called them "GM" engines. That's when I stopped buying GM products all together. I came back after the Pontiac engine works closed. I bought a 1994 Suburban and 1998 Malibu. I got 13 and 17 years out of those cars with no problems at all. There is definitely differences between engines coming from different plants.

My wife cried when I sold the Malibu. I just got tired of looking at it. The headliner was coming down and the velour had dried up and flaked off of the back deck.The heater core leaked and I could never get the antifreeze smell out of the car.

Yes.

No two plants are exactly the same.

Back MANY years ago, Ford offered two 351 cu. in. V8 engines. They were supposed to be identical I believe. One was made in Cleveland,Ohio, and the other in Windsor Canada. I'm not sure which, but one was very good and the other, very bad. So yes, it's very possible to get the same engine made different ways.

That’s actually a really interesting question. Obviously the design and specs, the engineering, is the same. Many of the raw materials and components may be the same, too ( though that varies). 
But I would expect variation in the final quality if the culture of the workforce is different. If the factory culture believes that everyone is a team and responsible for quality (like the famous Toyota “andon cords”) you will get a better product than if the culture says the managers are in charge and the line workers just do what they are told. 

Hell Yes. 

If I remember the story correctly, There was a Honda Engine built in America and during the manufacturing process found a hairline undetectable fracture in a camshaft, that the Japanese counterpart did not have. 

Good thing the American plant discovered the problem before sending the cars to the dealers. But too late where they had to go back and replace a ton of camshafts on already completed cars. 

So yes.  The same engine can differ depending where it is built together. 

And not just manufacturing plants. It could be a particular parts supplier too.

It reminds me of the leaky GM Vortec engines with defective cylinder heads that came from Castech.

Absolutely.