"I'm not certain the flight would be safe if the other engine on the same side of the aircraft failed."
Any two engines on a 747 will deliver it safely to a destination. A 747 flight over the Pacific a few years ago, destination Japan, had an engine go out, then a 2nd engine quit, then a 3rd engine shut down - the plane landed safely.
The 747 is "over-engineered" for safety. It has lifting capacity well in excess of its payload in cubic feet. Many space shuttle flights ended on a runway in California - the shuttles were all piggy-backed to Cape Canaveral on a 747. The only engineering differences between that 747 and the ones we might fly were the "brackets" or "attachments" to hold the shuttle in place.
About 25 years ago I was on a BA 747 bound from Los Angeles to London. Over Las Vegas the pilot announced that a problem with loss of oil pressure in the #3 engine meant that they had had to shut it down. He told us that we had reduced altitude to 24,000 ft and that we had a new destination - New York, saying that they obviously did not want to fly out over the ocean on three engines. We landed at JFK, were put up in a hotel for about 5 hours while they replaced the engine, then we continued on to London, same plane. Much more prudent than dumping fuel and returning to LA. I also think that this would have been much more prudent than continuing on across the Atlantic on the three engines. Saying that, I do not question the 747's capabilities.
BA 747's used Rolls Royce engines 25 years ago, I assume that is still true, but I don't know. Are those engines more suseptible to problems? I see this same plane had a recurrance of engine problems a couple weeks later. Besides my experience related here, I know personally of another instance where a BA 747 had to make an unscheduled landing because of engine failure - in Nairobi, on a flight from London to South Africa. The interesting part of that is that a replacement engine was flown into Nairobi to replace the failed engine, and the replaced engine was strapped onto the wing of that 747 for the continuation of that flight to Johannesburg.